




'''simple docstring'''





from typing import List, Optional, Tuple, Union

import torch

from ...models import UNetaDModel
from ...schedulers import KarrasVeScheduler
from ...utils import randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput




class  _snake_case		(	lowerCAmelCase_							):
			lowerCAmelCase_     :      UNetaDModel
			lowerCAmelCase_     :      KarrasVeScheduler




			def __init__(					self				,							a__				,							a__							)				->				Dict:

										'''simple docstring'''




										super().__init__()
										self.register_modules(unet=__lowerCAmelCase				,							scheduler=__lowerCAmelCase							)




			@torch.no_grad()
			def __call__(					self				,							a__ = 1				,							a__ = 50				,							a__ = None				,							a__ = "pil"				,							a__ = True				,							**a__				,							)				->				Optional[Any]:

										'''simple docstring'''




										snake_case_						=      self.unet.config.sample_size
										snake_case_						=      (batch_size, 3, img_size, img_size)

										snake_case_						=      self.unet

										# sample x_0 ~ N(0, sigma_0^2 * I)
										snake_case_						=      randn_tensor(__lowerCAmelCase				,							generator=__lowerCAmelCase				,							device=self.device							) * self.scheduler.init_noise_sigma

										self.scheduler.set_timesteps(__lowerCAmelCase							)

										for t in self.progress_bar(self.scheduler.timesteps							):
																	# here sigma_t == t_i from the paper
																	snake_case_						=      self.scheduler.schedule[t]
																	snake_case_						=      self.scheduler.schedule[t - 1] if t > 0 else 0

																	# 1. Select temporarily increased noise level sigma_hat
																	# 2. Add new noise to move from sample_i to sample_hat
																	snake_case_					,      snake_case_						=      self.scheduler.add_noise_to_input(__lowerCAmelCase				,							__lowerCAmelCase				,							generator=__lowerCAmelCase							)

																	# 3. Predict the noise residual given the noise magnitude `sigma_hat`
																	# The model inputs and output are adjusted by following eq. (213) in [1].
																	snake_case_						=      (sigma_hat / 2) * model((sample_hat + 1) / 2				,							sigma_hat / 2							).sample

																	# 4. Evaluate dx/dt at sigma_hat
																	# 5. Take Euler step from sigma to sigma_prev
																	snake_case_						=      self.scheduler.step(__lowerCAmelCase				,							__lowerCAmelCase				,							__lowerCAmelCase				,							__lowerCAmelCase							)

																	if sigma_prev != 0:
																								# 6. Apply 2nd order correction
																								# The model inputs and output are adjusted by following eq. (213) in [1].
																								snake_case_						=      (sigma_prev / 2) * model((step_output.prev_sample + 1) / 2				,							sigma_prev / 2							).sample
																								snake_case_						=      self.scheduler.step_correct(
																								    __lowerCAmelCase				,							__lowerCAmelCase				,							__lowerCAmelCase				,							__lowerCAmelCase				,							step_output.prev_sample				,							step_output["derivative"]				,							)
																	snake_case_						=      step_output.prev_sample

										snake_case_						=      (sample / 2 + 0.5).clamp(0				,							1							)
										snake_case_						=      sample.cpu().permute(0				,							2				,							3				,							1							).numpy()
										if output_type == "pil":
																	snake_case_						=      self.numpy_to_pil(__lowerCAmelCase							)

										if not return_dict:
																	return (image,)

										return ImagePipelineOutput(images=__lowerCAmelCase							)





"""simple docstring"""


from math import pow






def 			__UpperCAmelCase    (	lowercase      ,lowercase      ,lowercase      ,lowercase      ,lowercase      ,):







  """simple docstring"""
  if current_sum == needed_sum:
    # If the sum of the powers is equal to needed_sum, then we have a solution.
    solutions_count += 1
    return current_sum, solutions_count

  _UpperCAmelCase         =					int(pow(lowercase      ,lowercase						)						)
  if current_sum + i_to_n <= needed_sum:
    # If the sum of the powers is less than needed_sum, then continue adding powers.
    current_sum += i_to_n
    _UpperCAmelCase       , _UpperCAmelCase         =					backtrack(
        lowercase      ,lowercase      ,current_number + 1      ,lowercase      ,lowercase						)
    current_sum -= i_to_n
  if i_to_n < needed_sum:
    # If the power of i is less than needed_sum, then try with the next power.
    _UpperCAmelCase       , _UpperCAmelCase         =					backtrack(
        lowercase      ,lowercase      ,current_number + 1      ,lowercase      ,lowercase						)
  return current_sum, solutions_count






def 			__UpperCAmelCase    (	lowercase      ,lowercase						):







  """simple docstring"""
  if not (1 <= needed_sum <= 10_00 and 2 <= power <= 10):
    raise ValueError(
        """Invalid input\n"""
        """needed_sum must be between 1 and 1000, power between 2 and 10."""						)

  return backtrack(lowercase      ,lowercase      ,1      ,0      ,0						)[1]  # Return the solutions_count


if __name__ == "__main__":
    import doctest

    doctest.testmod()
