






'''simple docstring'''







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 		UpperCamelCase__    (snake_case__			):




		'''simple docstring'''





		_UpperCamelCase				  =					42
		_UpperCamelCase				  =					None



def 						A__			(				__lowerCAmelCase		:			Union[str, Any]   ,    __lowerCAmelCase		:			int=0.999   ,    __lowerCAmelCase		:			List[str]="cosine"   ,    ):
						if alpha_transform_type == "cosine":

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

						elif alpha_transform_type == "exp":

												def alpha_bar_fn(__lowerCAmelCase		:			List[str]						):
																		return math.exp(t * -12.0						)

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

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





class 		UpperCamelCase__    (snake_case__   ,snake_case__			):




		'''simple docstring'''





		@register_to_config
		def __init__(      self   ,_lowerCAmelCase = 10_00   ,_lowerCAmelCase = "fixed_small_log"   ,_lowerCAmelCase = True   ,_lowerCAmelCase = 1.0   ,_lowerCAmelCase = "epsilon"   ,_lowerCAmelCase = "squaredcos_cap_v2"   ,):



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

								lowerCamelCase__         =  betas_for_alpha_bar(UpperCAmelCase_       )

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

								# standard deviation of the initial noise distribution
								lowerCamelCase__         =  1.0

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

								lowerCamelCase__         =  variance_type






		def 			UpperCamelCase_					(      self   ,_lowerCAmelCase   ,_lowerCAmelCase = None       ):
								return sample






		def 			UpperCamelCase_					(      self   ,_lowerCAmelCase   ,_lowerCAmelCase = None       ):
								lowerCamelCase__         =  num_inference_steps
								lowerCamelCase__         =  (self.config.num_train_timesteps - 1) / (self.num_inference_steps - 1)
								lowerCamelCase__         =  (np.arange(0   ,UpperCAmelCase_       ) * step_ratio).round()[::-1].copy().astype(np.intaa       )
								lowerCamelCase__         =  torch.from_numpy(UpperCAmelCase_       ).to(UpperCAmelCase_       )






		def 			UpperCamelCase_					(      self   ,_lowerCAmelCase   ,_lowerCAmelCase=None   ,_lowerCAmelCase=None   ,_lowerCAmelCase=None       ):



								if prev_timestep is None:
														lowerCamelCase__         =  t - 1

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

								if prev_timestep == t - 1:
														lowerCamelCase__         =  self.betas[t]
								else:
														lowerCamelCase__         =  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
								lowerCamelCase__         =  beta_prod_t_prev / beta_prod_t * beta

								if variance_type is None:
														lowerCamelCase__         =  self.config.variance_type

								# hacks - were probably added for training stability
								if variance_type == "fixed_small_log":
														lowerCamelCase__         =  torch.log(torch.clamp(UpperCAmelCase_   ,min=1E-20       )       )
														lowerCamelCase__         =  torch.exp(0.5 * variance       )
								elif variance_type == "learned_range":
														# NOTE difference with DDPM scheduler
														lowerCamelCase__         =  variance.log()
														lowerCamelCase__         =  beta.log()

														lowerCamelCase__         =  (predicted_variance + 1) / 2
														lowerCamelCase__         =  frac * max_log + (1 - frac) * min_log

								return variance






		def 			UpperCamelCase_					(      self   ,_lowerCAmelCase   ,_lowerCAmelCase   ,_lowerCAmelCase   ,_lowerCAmelCase = None   ,_lowerCAmelCase=None   ,_lowerCAmelCase = True   ,):
								lowerCamelCase__         =  timestep

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

								# 1. compute alphas, betas
								if prev_timestep is None:
														lowerCamelCase__         =  t - 1

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

								if prev_timestep == t - 1:
														lowerCamelCase__         =  self.betas[t]
														lowerCamelCase__         =  self.alphas[t]
								else:
														lowerCamelCase__         =  1 - alpha_prod_t / alpha_prod_t_prev
														lowerCamelCase__         =  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":
														lowerCamelCase__         =  (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
								elif self.config.prediction_type == "sample":
														lowerCamelCase__         =  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:
														lowerCamelCase__         =  torch.clamp(
														    UpperCAmelCase_   ,-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
								lowerCamelCase__         =  (alpha_prod_t_prev ** 0.5 * beta) / beta_prod_t
								lowerCamelCase__         =  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
								lowerCamelCase__         =  pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

								# 6. Add noise
								lowerCamelCase__         =  0
								if t > 0:
														lowerCamelCase__         =  randn_tensor(
														    model_output.shape   ,dtype=model_output.dtype   ,generator=UpperCAmelCase_   ,device=model_output.device       )

														lowerCamelCase__         =  self._get_variance(
														    UpperCAmelCase_   ,predicted_variance=UpperCAmelCase_   ,prev_timestep=UpperCAmelCase_   ,)

														if self.variance_type == "fixed_small_log":
																				lowerCamelCase__         =  variance
														elif self.variance_type == "learned_range":
																				lowerCamelCase__         =  (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."""       )

														lowerCamelCase__         =  variance * variance_noise

								lowerCamelCase__         =  pred_prev_sample + variance

								if not return_dict:
														return (pred_prev_sample,)

								return UnCLIPSchedulerOutput(prev_sample=UpperCAmelCase_   ,pred_original_sample=UpperCAmelCase_       )






		def 			UpperCamelCase_					(      self   ,_lowerCAmelCase   ,_lowerCAmelCase   ,_lowerCAmelCase   ,):
								lowerCamelCase__         =  self.alphas_cumprod.to(device=original_samples.device   ,dtype=original_samples.dtype       )
								lowerCamelCase__         =  timesteps.to(original_samples.device       )

								lowerCamelCase__         =  alphas_cumprod[timesteps] ** 0.5
								lowerCamelCase__         =  sqrt_alpha_prod.flatten()
								while len(sqrt_alpha_prod.shape       ) < len(original_samples.shape       ):
														lowerCamelCase__         =  sqrt_alpha_prod.unsqueeze(-1       )

								lowerCamelCase__         =  (1 - alphas_cumprod[timesteps]) ** 0.5
								lowerCamelCase__         =  sqrt_one_minus_alpha_prod.flatten()
								while len(sqrt_one_minus_alpha_prod.shape       ) < len(original_samples.shape       ):
														lowerCamelCase__         =  sqrt_one_minus_alpha_prod.unsqueeze(-1       )

								lowerCamelCase__         =  sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
								return noisy_samples









'''simple docstring'''







def 						A__			(				):
						return [
						    a * b * (1000 - a - b)
						    for a in range(1   ,    999						)
						    for b in range(__lowerCAmelCase   ,    999						)
						    if (a * a + b * b == (1000 - a - b) ** 2)
						][0]


if __name__ == "__main__":
							print(F'{solution() = }')

