




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 		lowercase							(     UpperCamelCase__	):
     _a											=		4_2
     _a											=		4_2

     def __init__(						self	,  _a	,  _a       )		->							int:
           super().__init__()
           self.register_modules(unet=_a	,  scheduler=_a       )



     @torch.no_grad()
     def __call__(						self	,  _a = 1	,  _a = 50	,  _a = None	,  _a = "pil"	,  _a = True	,  **_a	,  )		->							Union[Tuple, ImagePipelineOutput]:
           _A							:  int    =		self.unet.config.sample_size
           _A							:  Any    =		(batch_size, 3, img_size, img_size)

           _A							:  Optional[Any]    =		self.unet

           # sample x_0 ~ N(0, sigma_0^2 * I)
           _A							:  int    =		randn_tensor(_a	,  generator=_a	,  device=self.device       ) * self.scheduler.init_noise_sigma

           self.scheduler.set_timesteps(_a       )

           for t in self.progress_bar(self.scheduler.timesteps       ):
                 # here sigma_t == t_i from the paper
                 _A							:  int    =		self.scheduler.schedule[t]
                 _A							:  int    =		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
                 _A							:  Any    =		self.scheduler.add_noise_to_input(_a	,  _a	,  generator=_a       )

                 # 3. Predict the noise residual given the noise magnitude `sigma_hat`
                 # The model inputs and output are adjusted by following eq. (213) in [1].
                 _A							:  Tuple    =		(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
                 _A							:  Tuple    =		self.scheduler.step(_a	,  _a	,  _a	,  _a       )

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

           _A							:  Tuple    =		(sample / 2 + 0.5).clamp(0	,  1       )
           _A							:  Dict    =		sample.cpu().permute(0	,  2	,  3	,  1       ).numpy()
           if output_type == "pil":
                 _A							:  int    =		self.numpy_to_pil(_a       )

           if not return_dict:
                 return (image,)

           return ImagePipelineOutput(images=_a       )










from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean







def        lowerCAmelCase_			(  snake_case_  ):

      # A local function to see if a dot lands in the circle.
      def is_in_circle(snake_case_,snake_case_  ) -> bool:
            _A							:  List[str]    =		sqrt((x**2) + (y**2)  )
            # Our circle has a radius of 1, so a distance
            # greater than 1 would land outside the circle.
            return distance_from_centre <= 1

      # The proportion of guesses that landed in the circle
      _A							:  Optional[int]    =		mean(
          int(is_in_circle(uniform(-1.0,1.0  ),uniform(-1.0,1.0  )  )  )
          for _ in range(snake_case_  )  )
      # The ratio of the area for circle to square is pi/4.
      _A							:  List[str]    =		proportion * 4
      print(f'''The estimated value of pi is {pi_estimate}'''  )
      print(f'''The numpy value of pi is {pi}'''  )
      print(f'''The total error is {abs(pi - pi_estimate  )}'''  )







def        lowerCAmelCase_			(  snake_case_,snake_case_,snake_case_ = 0.0,snake_case_ = 1.0,):
      return mean(
          function_to_integrate(uniform(snake_case_,snake_case_  )  ) for _ in range(snake_case_  )  ) * (max_value - min_value)







def        lowerCAmelCase_			(  snake_case_,snake_case_ = 0.0,snake_case_ = 1.0  ):

      def identity_function(snake_case_  ) -> float:
            return x

      _A							:  Any    =		area_under_curve_estimator(
          snake_case_,snake_case_,snake_case_,snake_case_  )
      _A							:  Tuple    =		(max_value * max_value - min_value * min_value) / 2

      print("""******************"""  )
      print(f'''Estimating area under y=x where x varies from {min_value} to {max_value}'''  )
      print(f'''Estimated value is {estimated_value}'''  )
      print(f'''Expected value is {expected_value}'''  )
      print(f'''Total error is {abs(estimated_value - expected_value  )}'''  )
      print("""******************"""  )







def        lowerCAmelCase_			(  snake_case_  ):

      def function_to_integrate(snake_case_  ) -> float:
            return sqrt(4.0 - x * x  )

      _A							:  Optional[int]    =		area_under_curve_estimator(
          snake_case_,snake_case_,0.0,2.0  )

      print("""******************"""  )
      print("""Estimating pi using area_under_curve_estimator"""  )
      print(f'''Estimated value is {estimated_value}'''  )
      print(f'''Expected value is {pi}'''  )
      print(f'''Total error is {abs(estimated_value - pi  )}'''  )
      print("""******************"""  )


if __name__ == "__main__":
  import doctest

  doctest.testmod()

