


from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, logging, randn_tensor
from .scheduling_utils import SchedulerMixin


lowerCamelCase		      = logging.get_logger(__name__)  # pylint: disable=invalid-name




@dataclass
class A						(     lowerCamelCase__  ):
						UpperCamelCase__							:						Tuple   =42




class A						(     lowerCamelCase__					,							lowerCamelCase__  ):
						UpperCamelCase__							:						Union[str, Any]   =1






						@register_to_config
						def __init__(      self		:  Optional[Any]    ,     lowercase_		:  int = 40    ,     lowercase_		:  float = 0.002    ,     lowercase_		:  float = 80.0    ,     lowercase_		:  float = 0.5    ,     lowercase_		:  float = 1.0    ,     lowercase_		:  float = 7.0    ,     lowercase_		:  bool = True    ,     )      ->		Union[str, Any]:
													"""simple docstring"""




													_lowerCamelCase :	Any						=sigma_max

													_lowerCamelCase :	int						=np.linspace(0    ,     1    ,     SCREAMING_SNAKE_CASE_				)
													_lowerCamelCase :	Optional[int]						=self._convert_to_karras(SCREAMING_SNAKE_CASE_				)
													_lowerCamelCase :	List[Any]						=self.sigma_to_t(SCREAMING_SNAKE_CASE_				)

													# setable values
													_lowerCamelCase :	str						=None
													_lowerCamelCase :	int						=torch.from_numpy(SCREAMING_SNAKE_CASE_				)
													_lowerCamelCase :	Any						=torch.from_numpy(SCREAMING_SNAKE_CASE_				)
													_lowerCamelCase :	Dict						=False
													_lowerCamelCase :	List[str]						=False






						def  lowerCamelCase (      self		:  Union[str, Any]    ,     lowercase_		:  Tuple    ,     lowercase_		:  List[str]=None				)      ->		List[Any]:
													"""simple docstring"""




													if schedule_timesteps is None:
																				_lowerCamelCase :	Tuple						=self.timesteps

													_lowerCamelCase :	Tuple						=(schedule_timesteps == timestep).nonzero()
													return indices.item()






						def  lowerCamelCase (      self		:  str    ,     lowercase_		:  torch.FloatTensor    ,     lowercase_		:  Union[float, torch.FloatTensor]				)      ->		Any:
													"""simple docstring"""




													if isinstance(SCREAMING_SNAKE_CASE_    ,     torch.Tensor				):
																				_lowerCamelCase :	Tuple						=timestep.to(self.timesteps.device				)
													_lowerCamelCase :	Union[str, Any]						=self.index_for_timestep(SCREAMING_SNAKE_CASE_				)
													_lowerCamelCase :	List[Any]						=self.sigmas[step_idx]

													_lowerCamelCase :	Union[str, Any]						=sample / ((sigma**2 + self.config.sigma_data**2) ** 0.5)

													_lowerCamelCase :	List[Any]						=True
													return sample






						def  lowerCamelCase (      self		:  Union[str, Any]    ,     lowercase_		:  Union[float, np.ndarray]				)      ->		int:
													"""simple docstring"""




													if not isinstance(SCREAMING_SNAKE_CASE_    ,     np.ndarray				):
																				_lowerCamelCase :	str						=np.array(SCREAMING_SNAKE_CASE_    ,     dtype=np.floataa				)

													_lowerCamelCase :	Optional[int]						=1000 * 0.25 * np.log(sigmas + 1E-44				)

													return timesteps






						def  lowerCamelCase (      self		:  Tuple    ,     lowercase_		:  Optional[int] = None    ,     lowercase_		:  Union[str, torch.device] = None    ,     lowercase_		:  Optional[List[int]] = None    ,     )      ->		Tuple:
													"""simple docstring"""




													if num_inference_steps is None and timesteps is None:
																				raise ValueError('Exactly one of `num_inference_steps` or `timesteps` must be supplied.'				)

													if num_inference_steps is not None and timesteps is not None:
																				raise ValueError('Can only pass one of `num_inference_steps` or `timesteps`.'				)

													# Follow DDPMScheduler custom timesteps logic
													if timesteps is not None:
																				for i in range(1    ,     len(SCREAMING_SNAKE_CASE_				)				):
																											if timesteps[i] >= timesteps[i - 1]:
																																		raise ValueError('`timesteps` must be in descending order.'				)

																				if timesteps[0] >= self.config.num_train_timesteps:
																											raise ValueError(
																											    F'''`timesteps` must start before `self.config.train_timesteps`:'''
																											    F''' {self.config.num_train_timesteps}.'''				)

																				_lowerCamelCase :	List[str]						=np.array(SCREAMING_SNAKE_CASE_    ,     dtype=np.intaa				)
																				_lowerCamelCase :	Dict						=True
													else:
																				if num_inference_steps > self.config.num_train_timesteps:
																											raise ValueError(
																											    F'''`num_inference_steps`: {num_inference_steps} cannot be larger than `self.config.train_timesteps`:'''
																											    F''' {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle'''
																											    F''' maximal {self.config.num_train_timesteps} timesteps.'''				)

																				_lowerCamelCase :	List[Any]						=num_inference_steps

																				_lowerCamelCase :	List[Any]						=self.config.num_train_timesteps // self.num_inference_steps
																				_lowerCamelCase :	Any						=(np.arange(0    ,     SCREAMING_SNAKE_CASE_				) * step_ratio).round()[::-1].copy().astype(np.intaa				)
																				_lowerCamelCase :	Optional[int]						=False

													# Map timesteps to Karras sigmas directly for multistep sampling
													# See https://github.com/openai/consistency_models/blob/main/cm/karras_diffusion.py#L675
													_lowerCamelCase :	Dict						=self.config.num_train_timesteps
													_lowerCamelCase :	Tuple						=timesteps[::-1].copy()
													_lowerCamelCase :	Union[str, Any]						=ramp / (num_train_timesteps - 1)
													_lowerCamelCase :	Tuple						=self._convert_to_karras(SCREAMING_SNAKE_CASE_				)
													_lowerCamelCase :	Optional[int]						=self.sigma_to_t(SCREAMING_SNAKE_CASE_				)

													_lowerCamelCase :	List[Any]						=np.concatenate([sigmas, [self.sigma_min]]				).astype(np.floataa				)
													_lowerCamelCase :	Optional[Any]						=torch.from_numpy(SCREAMING_SNAKE_CASE_				).to(device=SCREAMING_SNAKE_CASE_				)

													if str(SCREAMING_SNAKE_CASE_				).startswith('mps'				):
																				# mps does not support float64
																				_lowerCamelCase :	Any						=torch.from_numpy(SCREAMING_SNAKE_CASE_				).to(SCREAMING_SNAKE_CASE_    ,     dtype=torch.floataa				)
													else:
																				_lowerCamelCase :	Optional[Any]						=torch.from_numpy(SCREAMING_SNAKE_CASE_				).to(device=SCREAMING_SNAKE_CASE_				)






						def  lowerCamelCase (      self		:  Optional[int]    ,     lowercase_		:  int				)      ->		int:
													"""simple docstring"""




													_lowerCamelCase :	List[str]						=self.config.sigma_min
													_lowerCamelCase :	Tuple						=self.config.sigma_max

													_lowerCamelCase :	List[Any]						=self.config.rho
													_lowerCamelCase :	Tuple						=sigma_min ** (1 / rho)
													_lowerCamelCase :	List[Any]						=sigma_max ** (1 / rho)
													_lowerCamelCase :	Tuple						=(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
													return sigmas






						def  lowerCamelCase (      self		:  Dict    ,     lowercase_		:  Any				)      ->		int:
													"""simple docstring"""




													_lowerCamelCase :	int						=self.config.sigma_data

													_lowerCamelCase :	List[str]						=sigma_data**2 / (sigma**2 + sigma_data**2)
													_lowerCamelCase :	Any						=sigma * sigma_data / (sigma**2 + sigma_data**2) ** 0.5
													return c_skip, c_out






						def  lowerCamelCase (      self		:  int    ,     lowercase_		:  int				)      ->		str:
													"""simple docstring"""




													_lowerCamelCase :	Optional[int]						=self.config.sigma_min
													_lowerCamelCase :	List[str]						=self.config.sigma_data

													_lowerCamelCase :	Union[str, Any]						=sigma_data**2 / ((sigma - sigma_min) ** 2 + sigma_data**2)
													_lowerCamelCase :	Optional[int]						=(sigma - sigma_min) * sigma_data / (sigma**2 + sigma_data**2) ** 0.5
													return c_skip, c_out






						def  lowerCamelCase (      self		:  Optional[int]    ,     lowercase_		:  torch.FloatTensor    ,     lowercase_		:  Union[float, torch.FloatTensor]    ,     lowercase_		:  torch.FloatTensor    ,     lowercase_		:  Optional[torch.Generator] = None    ,     lowercase_		:  bool = True    ,     )      ->		Union[str, Any]:
													"""simple docstring"""




													if (
													    isinstance(SCREAMING_SNAKE_CASE_    ,     SCREAMING_SNAKE_CASE_				)
													    or isinstance(SCREAMING_SNAKE_CASE_    ,     torch.IntTensor				)
													    or isinstance(SCREAMING_SNAKE_CASE_    ,     torch.LongTensor				)
													):
																				raise ValueError(
																				    (
																				        'Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to'
																				        F''' `{self.__class__}.step()` is not supported. Make sure to pass'''
																				        ' one of the `scheduler.timesteps` as a timestep.'
																				    )    ,     )

													if not self.is_scale_input_called:
																				logger.warning(
																				    'The `scale_model_input` function should be called before `step` to ensure correct denoising. '
																				    'See `StableDiffusionPipeline` for a usage example.'				)

													if isinstance(SCREAMING_SNAKE_CASE_    ,     torch.Tensor				):
																				_lowerCamelCase :	List[str]						=timestep.to(self.timesteps.device				)

													_lowerCamelCase :	List[str]						=self.config.sigma_min
													_lowerCamelCase :	Optional[Any]						=self.config.sigma_max

													_lowerCamelCase :	List[Any]						=self.index_for_timestep(SCREAMING_SNAKE_CASE_				)

													# sigma_next corresponds to next_t in original implementation
													_lowerCamelCase :	Union[str, Any]						=self.sigmas[step_index]
													if step_index + 1 < self.config.num_train_timesteps:
																				_lowerCamelCase :	Dict						=self.sigmas[step_index + 1]
													else:
																				# Set sigma_next to sigma_min
																				_lowerCamelCase :	Tuple						=self.sigmas[-1]

													# Get scalings for boundary conditions
													_lowerCamelCase			,  _lowerCamelCase :	List[str]						=self.get_scalings_for_boundary_condition(SCREAMING_SNAKE_CASE_				)

													# 1. Denoise model output using boundary conditions
													_lowerCamelCase :	List[Any]						=c_out * model_output + c_skip * sample
													if self.config.clip_denoised:
																				_lowerCamelCase :	int						=denoised.clamp(-1    ,     1				)

													# 2. Sample z ~ N(0, s_noise^2 * I)
													# Noise is not used for onestep sampling.
													if len(self.timesteps				) > 1:
																				_lowerCamelCase :	Union[str, Any]						=randn_tensor(
																				    model_output.shape    ,     dtype=model_output.dtype    ,     device=model_output.device    ,     generator=SCREAMING_SNAKE_CASE_				)
													else:
																				_lowerCamelCase :	Tuple						=torch.zeros_like(SCREAMING_SNAKE_CASE_				)
													_lowerCamelCase :	Optional[int]						=noise * self.config.s_noise

													_lowerCamelCase :	List[Any]						=sigma_next.clamp(min=SCREAMING_SNAKE_CASE_    ,     max=SCREAMING_SNAKE_CASE_				)

													# 3. Return noisy sample
													# tau = sigma_hat, eps = sigma_min
													_lowerCamelCase :	Union[str, Any]						=denoised + z * (sigma_hat**2 - sigma_min**2) ** 0.5

													if not return_dict:
																				return (prev_sample,)

													return CMStochasticIterativeSchedulerOutput(prev_sample=SCREAMING_SNAKE_CASE_				)






						def  lowerCamelCase (      self		:  List[Any]    ,     lowercase_		:  torch.FloatTensor    ,     lowercase_		:  torch.FloatTensor    ,     lowercase_		:  torch.FloatTensor    ,     )      ->		Optional[int]:
													"""simple docstring"""




													_lowerCamelCase :	str						=self.sigmas.to(device=original_samples.device    ,     dtype=original_samples.dtype				)
													if original_samples.device.type == "mps" and torch.is_floating_point(SCREAMING_SNAKE_CASE_				):
																				# mps does not support float64
																				_lowerCamelCase :	int						=self.timesteps.to(original_samples.device    ,     dtype=torch.floataa				)
																				_lowerCamelCase :	str						=timesteps.to(original_samples.device    ,     dtype=torch.floataa				)
													else:
																				_lowerCamelCase :	Dict						=self.timesteps.to(original_samples.device				)
																				_lowerCamelCase :	Tuple						=timesteps.to(original_samples.device				)

													_lowerCamelCase :	Optional[Any]						=[(schedule_timesteps == t).nonzero().item() for t in timesteps]

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

													_lowerCamelCase :	List[str]						=original_samples + noise * sigma
													return noisy_samples






						def __len__(      self		:  List[Any]				)      ->		Dict:
													"""simple docstring"""




													return self.config.num_train_timesteps






from collections.abc import Callable

lowerCamelCase		      = Callable[[float], float]  # type alias for a real -> real function




def 			a_   (					SCREAMING_SNAKE_CASE__      :   RealFunc	,    SCREAMING_SNAKE_CASE__      :   RealFunc	,    SCREAMING_SNAKE_CASE__      :   int	,    ):
       '''simple docstring'''





       _lowerCamelCase :	Tuple						=float(SCREAMING_SNAKE_CASE__  )
       while True:
              try:
                     _lowerCamelCase :	int						=prev_guess - function(SCREAMING_SNAKE_CASE__  ) / derivative(SCREAMING_SNAKE_CASE__  )
              except ZeroDivisionError:
                     raise ZeroDivisionError('Could not find root'  ) from None
              if abs(prev_guess - next_guess  ) < 10**-5:
                     return next_guess
              _lowerCamelCase :	Union[str, Any]						=next_guess




def 			a_   (					SCREAMING_SNAKE_CASE__      :   float  ):
       '''simple docstring'''





       return (x**3) - (2 * x) - 5




def 			a_   (					SCREAMING_SNAKE_CASE__      :   float  ):
       '''simple docstring'''





       return 3 * (x**2) - 2


if __name__ == "__main__":
 print(newton(f, fa, 3))


