



'''simple docstring'''





import math
from collections import defaultdict
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput




def lowerCAmelCase						(__A						,			__A=0.9_99						,			__A="cosine"						,			):



					"""simple docstring"""



					if alpha_transform_type == "cosine":

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

					elif alpha_transform_type == "exp":

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

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

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






class __A    (						_UpperCAmelCase     ,     _UpperCAmelCase		):



	'''simple docstring'''







	__lowerCamelCase					: Optional[Any]    = [e.name for e in KarrasDiffusionSchedulers]
	__lowerCamelCase					: Tuple    = 2



	@register_to_config
	def __init__(self				,     A = 1_000				,     A = 0.00085				,     A = 0.012				,     A = "linear"				,     A = None				,     A = "epsilon"				,     A = False				,     A = False				,     A = 1.0				,     A = "linspace"				,     A = 0				,     )					->  Tuple:


						"""simple docstring"""



						if trained_betas is not None:
											_a											=						torch.tensor(lowerCamelCase_				,     dtype=torch.floataa )
						elif beta_schedule == "linear":
											_a											=						torch.linspace(lowerCamelCase_				,     lowerCamelCase_				,     lowerCamelCase_				,     dtype=torch.floataa )
						elif beta_schedule == "scaled_linear":
											# this schedule is very specific to the latent diffusion model.
											_a											=						(
											    torch.linspace(beta_start**0.5				,     beta_end**0.5				,     lowerCamelCase_				,     dtype=torch.floataa ) ** 2
											)
						elif beta_schedule == "squaredcos_cap_v2":
											# Glide cosine schedule
											_a											=						betas_for_alpha_bar(lowerCamelCase_				,     alpha_transform_type='''cosine''' )
						elif beta_schedule == "exp":
											_a											=						betas_for_alpha_bar(lowerCamelCase_				,     alpha_transform_type='''exp''' )
						else:
											raise NotImplementedError(f'''{beta_schedule} does is not implemented for {self.__class__}''' )

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

						#  set all values
						self.set_timesteps(lowerCamelCase_				,     lowerCamelCase_				,     lowerCamelCase_ )
						_a											=						use_karras_sigmas



	def       a__						(self				,     A				,     A=None )					->  Dict:


						"""simple docstring"""



						if schedule_timesteps is None:
											_a											=						self.timesteps

						_a											=						(schedule_timesteps == timestep).nonzero()

						# The sigma index that is taken for the **very** first `step`
						# is always the second index (or the last index if there is only 1)
						# This way we can ensure we don't accidentally skip a sigma in
						# case we start in the middle of the denoising schedule (e.g. for image-to-image)
						if len(self._index_counter ) == 0:
											_a											=						1 if len(lowerCamelCase_ ) > 1 else 0
						else:
											_a											=						timestep.cpu().item() if torch.is_tensor(lowerCamelCase_ ) else timestep
											_a											=						self._index_counter[timestep_int]

						return indices[pos].item()



	@property
	def       a__						(self )					->  str:


						"""simple docstring"""



						if self.config.timestep_spacing in ["linspace", "trailing"]:
											return self.sigmas.max()

						return (self.sigmas.max() ** 2 + 1) ** 0.5



	def       a__						(self				,     A				,     A				,     )					->  torch.FloatTensor:


						"""simple docstring"""



						_a											=						self.index_for_timestep(lowerCamelCase_ )

						_a											=						self.sigmas[step_index]
						_a											=						sample / ((sigma**2 + 1) ** 0.5)
						return sample



	def       a__						(self				,     A				,     A = None				,     A = None				,     )					->  str:


						"""simple docstring"""



						_a											=						num_inference_steps

						_a											=						num_train_timesteps or self.config.num_train_timesteps

						# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
						if self.config.timestep_spacing == "linspace":
											_a											=						np.linspace(0				,     num_train_timesteps - 1				,     lowerCamelCase_				,     dtype=lowerCamelCase_ )[::-1].copy()
						elif self.config.timestep_spacing == "leading":
											_a											=						num_train_timesteps // self.num_inference_steps
											# creates integer timesteps by multiplying by ratio
											# casting to int to avoid issues when num_inference_step is power of 3
											_a											=						(np.arange(0				,     lowerCamelCase_ ) * step_ratio).round()[::-1].copy().astype(lowerCamelCase_ )
											timesteps += self.config.steps_offset
						elif self.config.timestep_spacing == "trailing":
											_a											=						num_train_timesteps / self.num_inference_steps
											# creates integer timesteps by multiplying by ratio
											# casting to int to avoid issues when num_inference_step is power of 3
											_a											=						(np.arange(lowerCamelCase_				,     0				,     -step_ratio )).round().copy().astype(lowerCamelCase_ )
											timesteps -= 1
						else:
											raise ValueError(
											    f'''{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.''' )

						_a											=						np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5 )
						_a											=						np.log(lowerCamelCase_ )
						_a											=						np.interp(lowerCamelCase_				,     np.arange(0				,     len(lowerCamelCase_ ) )				,     lowerCamelCase_ )

						if self.config.use_karras_sigmas:
											_a											=						self._convert_to_karras(in_sigmas=lowerCamelCase_				,     num_inference_steps=self.num_inference_steps )
											_a											=						np.array([self._sigma_to_t(lowerCamelCase_				,     lowerCamelCase_ ) for sigma in sigmas] )

						_a											=						np.concatenate([sigmas, [0.0]] ).astype(np.floataa )
						_a											=						torch.from_numpy(lowerCamelCase_ ).to(device=lowerCamelCase_ )
						_a											=						torch.cat([sigmas[:1], sigmas[1:-1].repeat_interleave(2 ), sigmas[-1:]] )

						_a											=						torch.from_numpy(lowerCamelCase_ )
						_a											=						torch.cat([timesteps[:1], timesteps[1:].repeat_interleave(2 )] )

						if str(lowerCamelCase_ ).startswith('''mps''' ):
											# mps does not support float64
											_a											=						timesteps.to(lowerCamelCase_				,     dtype=torch.floataa )
						else:
											_a											=						timesteps.to(device=lowerCamelCase_ )

						# empty dt and derivative
						_a											=						None
						_a											=						None

						# for exp beta schedules, such as the one for `pipeline_shap_e.py`
						# we need an index counter
						_a											=						defaultdict(lowerCamelCase_ )



	def       a__						(self				,     A				,     A )					->  List[Any]:


						"""simple docstring"""



						_a											=						np.log(lowerCamelCase_ )

						# get distribution
						_a											=						log_sigma - log_sigmas[:, np.newaxis]

						# get sigmas range
						_a											=						np.cumsum((dists >= 0)				,     axis=0 ).argmax(axis=0 ).clip(max=log_sigmas.shape[0] - 2 )
						_a											=						low_idx + 1

						_a											=						log_sigmas[low_idx]
						_a											=						log_sigmas[high_idx]

						# interpolate sigmas
						_a											=						(low - log_sigma) / (low - high)
						_a											=						np.clip(lowerCamelCase_				,     0				,     1 )

						# transform interpolation to time range
						_a											=						(1 - w) * low_idx + w * high_idx
						_a											=						t.reshape(sigma.shape )
						return t



	def       a__						(self				,     A				,     A )					->  torch.FloatTensor:


						"""simple docstring"""



						_a											=						in_sigmas[-1].item()
						_a											=						in_sigmas[0].item()

						_a											=						7.0  # 7.0 is the value used in the paper
						_a											=						np.linspace(0				,     1				,     lowerCamelCase_ )
						_a											=						sigma_min ** (1 / rho)
						_a											=						sigma_max ** (1 / rho)
						_a											=						(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
						return sigmas



	@property
	def       a__						(self )					->  Optional[int]:


						"""simple docstring"""



						return self.dt is None



	def       a__						(self				,     A				,     A				,     A				,     A = True				,     )					->  Union[SchedulerOutput, Tuple]:


						"""simple docstring"""



						_a											=						self.index_for_timestep(lowerCamelCase_ )

						# advance index counter by 1
						_a											=						timestep.cpu().item() if torch.is_tensor(lowerCamelCase_ ) else timestep
						self._index_counter[timestep_int] += 1

						if self.state_in_first_order:
											_a											=						self.sigmas[step_index]
											_a											=						self.sigmas[step_index + 1]
						else:
											# 2nd order / Heun's method
											_a											=						self.sigmas[step_index - 1]
											_a											=						self.sigmas[step_index]

						# currently only gamma=0 is supported. This usually works best anyways.
						# We can support gamma in the future but then need to scale the timestep before
						# passing it to the model which requires a change in API
						_a											=						0
						_a											=						sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

						# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
						if self.config.prediction_type == "epsilon":
											_a											=						sigma_hat if self.state_in_first_order else sigma_next
											_a											=						sample - sigma_input * model_output
						elif self.config.prediction_type == "v_prediction":
											_a											=						sigma_hat if self.state_in_first_order else sigma_next
											_a											=						model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
											    sample / (sigma_input**2 + 1)
											)
						elif self.config.prediction_type == "sample":
											_a											=						model_output
						else:
											raise ValueError(
											    f'''prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`''' )

						if self.config.clip_sample:
											_a											=						pred_original_sample.clamp(
											    -self.config.clip_sample_range				,     self.config.clip_sample_range )

						if self.state_in_first_order:
											# 2. Convert to an ODE derivative for 1st order
											_a											=						(sample - pred_original_sample) / sigma_hat
											# 3. delta timestep
											_a											=						sigma_next - sigma_hat

											# store for 2nd order step
											_a											=						derivative
											_a											=						dt
											_a											=						sample
						else:
											# 2. 2nd order / Heun's method
											_a											=						(sample - pred_original_sample) / sigma_next
											_a											=						(self.prev_derivative + derivative) / 2

											# 3. take prev timestep & sample
											_a											=						self.dt
											_a											=						self.sample

											# free dt and derivative
											# Note, this puts the scheduler in "first order mode"
											_a											=						None
											_a											=						None
											_a											=						None

						_a											=						sample + derivative * dt

						if not return_dict:
											return (prev_sample,)

						return SchedulerOutput(prev_sample=lowerCamelCase_ )



	def       a__						(self				,     A				,     A				,     A				,     )					->  torch.FloatTensor:


						"""simple docstring"""



						_a											=						self.sigmas.to(device=original_samples.device				,     dtype=original_samples.dtype )
						if original_samples.device.type == "mps" and torch.is_floating_point(lowerCamelCase_ ):
											# mps does not support float64
											_a											=						self.timesteps.to(original_samples.device				,     dtype=torch.floataa )
											_a											=						timesteps.to(original_samples.device				,     dtype=torch.floataa )
						else:
											_a											=						self.timesteps.to(original_samples.device )
											_a											=						timesteps.to(original_samples.device )

						_a											=						[self.index_for_timestep(lowerCamelCase_				,     lowerCamelCase_ ) for t in timesteps]

						_a											=						sigmas[step_indices].flatten()
						while len(sigma.shape ) < len(original_samples.shape ):
											_a											=						sigma.unsqueeze(-1 )

						_a											=						original_samples + noise * sigma
						return noisy_samples



	def __len__(self )					->  int:


						"""simple docstring"""



						return self.config.num_train_timesteps








'''simple docstring'''





def lowerCAmelCase						(__A = 1_000):



     """simple docstring"""



     _a											=						2**power
     _a											=						str(__A)
     _a											=						list(__A)
     _a											=						0

     for i in list_num:
          sum_of_num += int(__A)

     return sum_of_num


if __name__ == "__main__":
  lowercase_	 =						int(input("Enter the power of 2: ").strip())
  print("2 ^ ", power, " = ", 2**power)
  lowercase_	 =						solution(power)
  print("Sum of the digits is: ", result)



