
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        lowerCAmelCase__      (   _lowerCamelCase	):
						UpperCamelCase_							: List[Any]	=		42
						UpperCamelCase_							: List[str]	=		42

						def __init__(			self       ,							a       ,							a				)					->      List[str]:


								'''simple docstring'''

								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]:


								'''simple docstring'''

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

								_UpperCamelCase						    =	self.unet

								# sample x_0 ~ N(0, sigma_0^2 * I)
								_UpperCamelCase						    =	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
										_UpperCamelCase						    =	self.scheduler.schedule[t]
										_UpperCamelCase						    =	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
										_UpperCamelCase    ,	_UpperCamelCase						    =	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].
										_UpperCamelCase						    =	(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
										_UpperCamelCase						    =	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].
												_UpperCamelCase						    =	(sigma_prev / 2) * model((step_output.prev_sample + 1) / 2       ,							sigma_prev / 2				).sample
												_UpperCamelCase						    =	self.scheduler.step_correct(
												    A__       ,							A__       ,							A__       ,							A__       ,							step_output.prev_sample       ,							step_output["""derivative"""]       ,							)
										_UpperCamelCase						    =	step_output.prev_sample

								_UpperCamelCase						    =	(sample / 2 + 0.5).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 (image,)

								return ImagePipelineOutput(images=A__				)







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


def 							__A(lowerCAmelCase						,  lowerCAmelCase						,  lowerCAmelCase = "x"						,  lowerCAmelCase = 1_0**-1_0						,  lowerCAmelCase = 1						,  )		->				complex:

		"""simple docstring"""






		_UpperCamelCase						    =	symbols(lowerCAmelCase )
		_UpperCamelCase						    =	lambdify(lowerCAmelCase						,  lowerCAmelCase )
		_UpperCamelCase						    =	lambdify(lowerCAmelCase						,  diff(lowerCAmelCase						,  lowerCAmelCase ) )

		_UpperCamelCase						    =	starting_point

		while True:
				if diff_function(lowerCAmelCase ) != 0:
						_UpperCamelCase						    =	prev_guess - multiplicity * func(lowerCAmelCase ) / diff_function(
						    lowerCAmelCase )
				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=0.0_05)}""",
		)

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



