



from typing import List, Optional, Tuple, Union

import torch

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







class     __lowerCAmelCase					(    A		):
			UpperCamelCase           =  42
			UpperCamelCase           =  42



			def __init__(		self     :						str				,	A     :						UNetaDModel				,	A     :						ScoreSdeVeScheduler)     ->					Any:



						"""simple docstring"""






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



			@torch.no_grad()
			def __call__(		self     :						Tuple				,	A     :						int = 1				,	A     :						int = 20_00				,	A     :						Optional[Union[torch.Generator, List[torch.Generator]]] = None				,	A     :						Optional[str] = "pil"				,	A     :						bool = True				,	**A     :						List[str]				,	)     ->					Union[ImagePipelineOutput, Tuple]:



						"""simple docstring"""






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

						_UpperCAmelCase	 =     self.unet

						_UpperCAmelCase	 =     randn_tensor(A				,	generator=A) * self.scheduler.init_noise_sigma
						_UpperCAmelCase	 =     sample.to(self.device)

						self.scheduler.set_timesteps(A)
						self.scheduler.set_sigmas(A)

						for i, t in enumerate(self.progress_bar(self.scheduler.timesteps)):
									_UpperCAmelCase	 =     self.scheduler.sigmas[i] * torch.ones(shape[0]				,	device=self.device)

									# correction step
									for _ in range(self.scheduler.config.correct_steps):
												_UpperCAmelCase	 =     self.unet(A				,	A).sample
												_UpperCAmelCase	 =     self.scheduler.step_correct(A				,	A				,	generator=A).prev_sample

									# prediction step
									_UpperCAmelCase	 =     model(A				,	A).sample
									_UpperCAmelCase	 =     self.scheduler.step_pred(A				,	A				,	A				,	generator=A)

									_UpperCAmelCase ,  _UpperCAmelCase	 =     output.prev_sample, output.prev_sample_mean

						_UpperCAmelCase	 =     sample_mean.clamp(0				,	1)
						_UpperCAmelCase	 =     sample.cpu().permute(0				,	2				,	3				,	1).numpy()
						if output_type == "pil":
									_UpperCAmelCase	 =     self.numpy_to_pil(A)

						if not return_dict:
									return (sample,)

						return ImagePipelineOutput(images=A)





from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403





def 							A			(  _UpperCAmelCase       :     str							,     _UpperCAmelCase       :     complex							,     _UpperCAmelCase       :     str = "x"							,     _UpperCAmelCase       :     float = 10**-10							,     _UpperCAmelCase       :     int = 1							,     )       ->				complex:







			'''simple docstring'''
			_UpperCAmelCase	 =     symbols(_UpperCAmelCase					)
			_UpperCAmelCase	 =     lambdify(_UpperCAmelCase							,     _UpperCAmelCase					)
			_UpperCAmelCase	 =     lambdify(_UpperCAmelCase							,     diff(_UpperCAmelCase							,     _UpperCAmelCase					)					)

			_UpperCAmelCase	 =     starting_point

			while True:
						if diff_function(_UpperCAmelCase					) != 0:
									_UpperCAmelCase	 =     prev_guess - multiplicity * func(_UpperCAmelCase					) / diff_function(
									    _UpperCAmelCase					)
						else:
									raise ZeroDivisionError('Could not find root'					) from None

						# Precision is checked by comparing the difference of consecutive guesses
						if abs(next_guess - prev_guess					) < precision:
									return next_guess

						_UpperCAmelCase	 =     next_guess


# Let's Execute
if __name__ == "__main__":
							# Find root of trigonometric function
							# Find value of pi
							print(f"""The root of sin(x) = 0 is {newton_raphson("sin(x)", 2)}""")

							# Find root of polynomial
							# Find fourth Root of 5
							print(f"""The root of x**4 - 5 = 0 is {newton_raphson("x**4 -5", 0.4 +5J)}""")

							# Find value of e
							print(
							    "The root of log(y) - 1 = 0 is ",
							    f"""{newton_raphson("log(y) - 1", 2, variable="y")}""",
							)

							# Exponential Roots
							print(
							    "The root of exp(x) - 1 = 0 is",
							    f"""{newton_raphson("exp(x) - 1", 10, precision=0.005)}""",
							)

							# Find root of cos(x)
							print(f"""The root of cos(x) = 0 is {newton_raphson("cos(x)", 0)}""")
