




"""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 					lowercase(     __a ):







 '''simple docstring'''





 lowercase__ 					=					42
 lowercase__ 					=					None







def 					UpperCAmelCase__       (snake_case__							:					str		,   snake_case__							:					List[Any]=0.9_99		,   snake_case__							:					Dict="cosine"		,   ):
  """simple docstring"""

  if alpha_transform_type == "cosine":

    def alpha_bar_fn(snake_case__							:					Dict    ):
      return math.cos((t + 0.0_08) / 1.0_08 * 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							:		int								=  []
  for i in range(snake_case__    ):
    _snake_case							:		Tuple								=  i / num_diffusion_timesteps
    _snake_case							:		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 					lowercase(     __a       ,			__a ):







 '''simple docstring'''





 @register_to_config
 def __init__(				self:		List[str],      a_:		int = 1_000,      a_:		str = "fixed_small_log",      a_:		bool = True,      a_:		Optional[float] = 1.0,      a_:		str = "epsilon",      a_:		str = "squaredcos_cap_v2",      ):




   '''simple docstring'''



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

   _snake_case							:		Tuple								=  betas_for_alpha_bar(a_		)

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

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

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

   _snake_case							:		int								=  variance_type


 def  UpperCamelCase_   (				self:		Dict,      a_:		torch.FloatTensor,      a_:		Optional[int] = None		):




   '''simple docstring'''



   return sample


 def  UpperCamelCase_   (				self:		Any,      a_:		int,      a_:		Union[str, torch.device] = None		):




   '''simple docstring'''



   _snake_case							:		List[Any]								=  num_inference_steps
   _snake_case							:		Any								=  (self.config.num_train_timesteps - 1) / (self.num_inference_steps - 1)
   _snake_case							:		Optional[int]								=  (np.arange(0,      a_		) * step_ratio).round()[::-1].copy().astype(np.intaa		)
   _snake_case							:		Optional[Any]								=  torch.from_numpy(a_		).to(a_		)


 def  UpperCamelCase_   (				self:		List[Any],      a_:		Tuple,      a_:		Dict=None,      a_:		Union[str, Any]=None,      a_:		Tuple=None		):




   '''simple docstring'''



   if prev_timestep is None:
     _snake_case							:		Optional[Any]								=  t - 1

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

   if prev_timestep == t - 1:
     _snake_case							:		int								=  self.betas[t]
   else:
     _snake_case							:		Union[str, 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
   _snake_case							:		int								=  beta_prod_t_prev / beta_prod_t * beta

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

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

     _snake_case							:		Optional[int]								=  (predicted_variance + 1) / 2
     _snake_case							:		Dict								=  frac * max_log + (1 - frac) * min_log

   return variance


 def  UpperCamelCase_   (				self:		Optional[Any],      a_:		torch.FloatTensor,      a_:		int,      a_:		torch.FloatTensor,      a_:		Optional[int] = None,      a_:		Tuple=None,      a_:		bool = True,      ):




   '''simple docstring'''



   _snake_case							:		List[Any]								=  timestep

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

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

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

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

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

     _snake_case							:		Union[str, Any]								=  self._get_variance(
         a_,      predicted_variance=a_,      prev_timestep=a_,      )

     if self.variance_type == "fixed_small_log":
       _snake_case							:		Tuple								=  variance
     elif self.variance_type == "learned_range":
       _snake_case							:		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."""		)

     _snake_case							:		List[Any]								=  variance * variance_noise

   _snake_case							:		Any								=  pred_prev_sample + variance

   if not return_dict:
     return (pred_prev_sample,)

   return UnCLIPSchedulerOutput(prev_sample=a_,      pred_original_sample=a_		)


 def  UpperCamelCase_   (				self:		Union[str, Any],      a_:		torch.FloatTensor,      a_:		torch.FloatTensor,      a_:		torch.IntTensor,      ):




   '''simple docstring'''



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

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

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

   _snake_case							:		Any								=  sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
   return noisy_samples








"""simple docstring"""


from math import factorial

A_						=				{str(d): factorial(d) for d in range(10)}


def 					UpperCAmelCase__       (snake_case__							:					int    ):
  """simple docstring"""

  return sum(DIGIT_FACTORIAL[d] for d in str(snake_case__    )    )


def 					UpperCAmelCase__       ():
  """simple docstring"""

  _snake_case							:		List[str]								=  7 * factorial(9    ) + 1
  return sum(i for i in range(3		,   snake_case__    ) if sum_of_digit_factorial(snake_case__    ) == i    )


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


