


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        lowerCAmelCase__ (					_A  ):






						"""simple docstring"""
						__UpperCAmelCase       :						torch.FloatTensor
						__UpperCAmelCase       :						Optional[torch.FloatTensor]    	=			None







def 							__magic_name__    (     lowerCAmelCase_     ,	lowerCAmelCase_=0.9_99     ,	lowerCAmelCase_="cosine"     ,	):
	'''simple docstring'''


	if alpha_transform_type == "cosine":

		def alpha_bar_fn(lowerCAmelCase_):
			return math.cos((t + 0.0_08) / 1.0_08 * math.pi / 2) ** 2

	elif alpha_transform_type == "exp":

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

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

	lowerCamelCase_					:				Optional[Any]              =  []
	for i in range(_snake_case):
		lowerCamelCase_					:				Optional[Any]              =  i / num_diffusion_timesteps
		lowerCamelCase_					:				Union[str, Any]              =  (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        lowerCAmelCase__ (					_A,							_A  ):






						"""simple docstring"""




						@register_to_config
						def __init__(       self ,				a_ = 1000 ,				a_ = "fixed_small_log" ,				a_ = True ,				a_ = 1.0 ,				a_ = "epsilon" ,				a_ = "squaredcos_cap_v2" ,				):
							if beta_schedule != "squaredcos_cap_v2":
								raise ValueError("UnCLIPScheduler only supports `beta_schedule`: \'squaredcos_cap_v2\'"      )

							lowerCamelCase_					:				Optional[int]              =  betas_for_alpha_bar(__lowerCAmelCase      )

							lowerCamelCase_					:				Tuple              =  1.0 - self.betas
							lowerCamelCase_					:				int              =  torch.cumprod(self.alphas ,				dim=0      )
							lowerCamelCase_					:				Tuple              =  torch.tensor(1.0      )

							# standard deviation of the initial noise distribution
							lowerCamelCase_					:				Optional[Any]              =  1.0

							# setable values
							lowerCamelCase_					:				List[str]              =  None
							lowerCamelCase_					:				Optional[Any]              =  torch.from_numpy(np.arange(0 ,				__lowerCAmelCase      )[::-1].copy()      )

							lowerCamelCase_					:				int              =  variance_type




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




						def 	_UpperCamelCase					(       self ,				a_ ,				a_ = None      ):
							lowerCamelCase_					:				List[str]              =  num_inference_steps
							lowerCamelCase_					:				int              =  (self.config.num_train_timesteps - 1) / (self.num_inference_steps - 1)
							lowerCamelCase_					:				Optional[int]              =  (np.arange(0 ,				__lowerCAmelCase      ) * step_ratio).round()[::-1].copy().astype(np.intaa      )
							lowerCamelCase_					:				Union[str, Any]              =  torch.from_numpy(__lowerCAmelCase      ).to(__lowerCAmelCase      )




						def 	_UpperCamelCase					(       self ,				a_ ,				a_=None ,				a_=None ,				a_=None      ):
							if prev_timestep is None:
								lowerCamelCase_					:				Any              =  t - 1

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

							if prev_timestep == t - 1:
								lowerCamelCase_					:				str              =  self.betas[t]
							else:
								lowerCamelCase_					:				Tuple              =  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_					:				Union[str, Any]              =  beta_prod_t_prev / beta_prod_t * beta

							if variance_type is None:
								lowerCamelCase_					:				Any              =  self.config.variance_type

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

								lowerCamelCase_					:				Union[str, Any]              =  (predicted_variance + 1) / 2
								lowerCamelCase_					:				Tuple              =  frac * max_log + (1 - frac) * min_log

							return variance




						def 	_UpperCamelCase					(       self ,				a_ ,				a_ ,				a_ ,				a_ = None ,				a_=None ,				a_ = True ,				):
							lowerCamelCase_					:				Any              =  timestep

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

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

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

							if prev_timestep == t - 1:
								lowerCamelCase_					:				str              =  self.betas[t]
								lowerCamelCase_					:				Any              =  self.alphas[t]
							else:
								lowerCamelCase_					:				str              =  1 - alpha_prod_t / alpha_prod_t_prev
								lowerCamelCase_					:				Dict              =  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_					:				Dict              =  (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
							elif self.config.prediction_type == "sample":
								lowerCamelCase_					:				Tuple              =  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_					:				str              =  torch.clamp(
								    __lowerCAmelCase ,				-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_					:				Any              =  (alpha_prod_t_prev ** 0.5 * beta) / beta_prod_t
							lowerCamelCase_					:				Tuple              =  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_					:				Union[str, Any]              =  pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

							# 6. Add noise
							lowerCamelCase_					:				Dict              =  0
							if t > 0:
								lowerCamelCase_					:				str              =  randn_tensor(
								    model_output.shape ,				dtype=model_output.dtype ,				generator=__lowerCAmelCase ,				device=model_output.device      )

								lowerCamelCase_					:				Dict              =  self._get_variance(
								    __lowerCAmelCase ,				predicted_variance=__lowerCAmelCase ,				prev_timestep=__lowerCAmelCase ,				)

								if self.variance_type == "fixed_small_log":
									lowerCamelCase_					:				Tuple              =  variance
								elif self.variance_type == "learned_range":
									lowerCamelCase_					:				Union[str, Any]              =  (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_					:				Tuple              =  variance * variance_noise

							lowerCamelCase_					:				List[str]              =  pred_prev_sample + variance

							if not return_dict:
								return (pred_prev_sample,)

							return UnCLIPSchedulerOutput(prev_sample=__lowerCAmelCase ,				pred_original_sample=__lowerCAmelCase      )




						def 	_UpperCamelCase					(       self ,				a_ ,				a_ ,				a_ ,				):
							# Make sure alphas_cumprod and timestep have same device and dtype as original_samples
							lowerCamelCase_					:				Any              =  self.alphas_cumprod.to(device=original_samples.device ,				dtype=original_samples.dtype      )
							lowerCamelCase_					:				List[str]              =  timesteps.to(original_samples.device      )

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

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

							lowerCamelCase_					:				List[Any]              =  sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
							return noisy_samples






import itertools
import math

def 	SCREAMING_SNAKE_CASE_							(	_snake_case	:int				)  ->     bool:

   if 1 < number < 4:
      # 2 and 3 are primes
      return True
   elif number < 2 or number % 2 == 0 or number % 3 == 0:
      # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
      return False

   # All primes number are in format of 6k +/- 1
   for i in range(5	,   int(math.sqrt(_snake_case				) + 1				)	,   6				):
      if number % i == 0 or number % (i + 2) == 0:
         return False
   return True

def 	SCREAMING_SNAKE_CASE_							(	)  ->     Dict:
   _A      =       2
   while True:
      if is_prime(_snake_case				):
         yield num
      num += 1

def 	SCREAMING_SNAKE_CASE_							(	_snake_case	:int = 10_001				)  ->     int:
   return next(itertools.islice(prime_generator()	,   nth - 1	,   _snake_case				)				)


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



