






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_  (		__lowercase		):
     __lowerCamelCase      				=  42
     __lowerCamelCase      				=  None





def  _lowerCamelCase						(						__lowerCamelCase ,							__lowerCamelCase=0.999 ,							__lowerCamelCase="cosine" ,							) ->			int:

     '''simple docstring'''


     if alpha_transform_type == "cosine":

          def alpha_bar_fn(__lowerCamelCase       ):
               return math.cos((t + 0.008) / 1.008 * 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}"       )

     UpperCAmelCase__      :  Dict				      =			[]
     for i in range(_lowerCamelCase       ):
          UpperCAmelCase__      :  List[Any]				      =			i / num_diffusion_timesteps
          UpperCAmelCase__      :  str				      =			(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 				UpperCAmelCase_  (		__lowercase							,      __lowercase		):




     @register_to_config
     def __init__(				self	,						_lowerCAmelCase = 1000	,						_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'"""		)

          UpperCAmelCase__      :  Optional[int]				      =			betas_for_alpha_bar(_lowerCAmelCase		)

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

          # standard deviation of the initial noise distribution
          UpperCAmelCase__      :  int				      =			1.0

          # setable values
          UpperCAmelCase__      :  Union[str, Any]				      =			None
          UpperCAmelCase__      :  Any				      =			torch.from_numpy(np.arange(0	,						_lowerCAmelCase		)[::-1].copy()		)

          UpperCAmelCase__      :  Optional[Any]				      =			variance_type




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




     def   __UpperCAmelCase  (				self	,						_lowerCAmelCase	,						_lowerCAmelCase = None		):
          UpperCAmelCase__      :  Optional[Any]				      =			num_inference_steps
          UpperCAmelCase__      :  Optional[int]				      =			(self.config.num_train_timesteps - 1) / (self.num_inference_steps - 1)
          UpperCAmelCase__      :  int				      =			(np.arange(0	,						_lowerCAmelCase		) * step_ratio).round()[::-1].copy().astype(np.intaa		)
          UpperCAmelCase__      :  str				      =			torch.from_numpy(_lowerCAmelCase		).to(_lowerCAmelCase		)




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

          if prev_timestep is None:
               UpperCAmelCase__      :  Union[str, Any]				      =			t - 1

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

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

          if variance_type is None:
               UpperCAmelCase__      :  Optional[int]				      =			self.config.variance_type

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

               UpperCAmelCase__      :  int				      =			(predicted_variance + 1) / 2
               UpperCAmelCase__      :  Tuple				      =			frac * max_log + (1 - frac) * min_log

          return variance




     def   __UpperCAmelCase  (				self	,						_lowerCAmelCase	,						_lowerCAmelCase	,						_lowerCAmelCase	,						_lowerCAmelCase = None	,						_lowerCAmelCase=None	,						_lowerCAmelCase = True	,						):
          UpperCAmelCase__      :  Any				      =			timestep

          if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type == "learned_range":
               UpperCAmelCase__      :  Optional[Any]				      =			torch.split(_lowerCAmelCase	,						sample.shape[1]	,						dim=1		)
          else:
               UpperCAmelCase__      :  Tuple				      =			None

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

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

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

          # 6. Add noise
          UpperCAmelCase__      :  List[str]				      =			0
          if t > 0:
               UpperCAmelCase__      :  Dict				      =			randn_tensor(
                   model_output.shape	,						dtype=model_output.dtype	,						generator=_lowerCAmelCase	,						device=model_output.device		)

               UpperCAmelCase__      :  Union[str, Any]				      =			self._get_variance(
                   _lowerCAmelCase	,						predicted_variance=_lowerCAmelCase	,						prev_timestep=_lowerCAmelCase	,						)

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

               UpperCAmelCase__      :  List[Any]				      =			variance * variance_noise

          UpperCAmelCase__      :  int				      =			pred_prev_sample + variance

          if not return_dict:
               return (pred_prev_sample,)

          return UnCLIPSchedulerOutput(prev_sample=_lowerCAmelCase	,						pred_original_sample=_lowerCAmelCase		)




     def   __UpperCAmelCase  (				self	,						_lowerCAmelCase	,						_lowerCAmelCase	,						_lowerCAmelCase	,						):
          UpperCAmelCase__      :  str				      =			self.alphas_cumprod.to(device=original_samples.device	,						dtype=original_samples.dtype		)
          UpperCAmelCase__      :  Tuple				      =			timesteps.to(original_samples.device		)

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

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

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













'''simple docstring'''






def 					_a						(       _lowerCamelCase = 100 ) ->				int:



			"""simple docstring"""


			__snake_case					:      Any							      =     n * (n + 1) * (2 * n + 1) / 6
			__snake_case					:      List[Any]							      =     (n * (n + 1) / 2) ** 2
			return int(square_of_sum - sum_of_squares )


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


