


'''simple docstring'''
from __future__ import annotations

from decimal import Decimal
from math import *  # noqa: F403

from sympy import diff





def 					a__       (					lowerCAmelCase__  ,					lowerCAmelCase__  ,					lowerCAmelCase__ = 10**-10						)    ->	float:
    UpperCAmelCase__			:		str													=				a
    while True:
        UpperCAmelCase__			:		Dict													=				Decimal(lowerCAmelCase__						) - (
            Decimal(eval(lowerCAmelCase__						)						) / Decimal(eval(str(diff(lowerCAmelCase__						)						)						)						)  # noqa: S307
        )
        # This number dictates the accuracy of the answer
        if abs(eval(lowerCAmelCase__						)						) < precision:  # noqa: S307
            return float(lowerCAmelCase__						)


# 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
  print(F"""The root of x**2 - 5*x + 2 = 0 is {newton_raphson('x**2 - 5*x + 2', 0.4)}""")
  # Find Square Root of 5
  print(F"""The root of log(x) - 1 = 0 is {newton_raphson('log(x) - 1', 2)}""")
  # Exponential Roots
  print(F"""The root of exp(x) - 1 = 0 is {newton_raphson('exp(x) - 1', 0)}""")




'''simple docstring'''
from typing import List, Optional, Tuple, Union

import torch

from ...utils import logging, randn_tensor
from ..pipeline_utils import AudioPipelineOutput, DiffusionPipeline


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




class 			lowerCamelCase_   (	__a      ):






      def __init__(					self				:    Any						,						_A				:    int						,						_A				:    str ):


          '''simple docstring'''


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






      @torch.no_grad()
      def __call__(					self				:    Union[str, Any]						,						_A				:    int = 1						,						_A				:    int = 100						,						_A				:    Optional[Union[torch.Generator, List[torch.Generator]]] = None						,						_A				:    Optional[float] = None						,						_A				:    bool = True						,						):


          '''simple docstring'''


          if audio_length_in_s is None:
              UpperCAmelCase__			:		List[str]													=				self.unet.config.sample_size / self.unet.config.sample_rate

          UpperCAmelCase__			:		Dict													=				audio_length_in_s * self.unet.config.sample_rate

          UpperCAmelCase__			:		Union[str, Any]													=				2 ** len(self.unet.up_blocks )
          if sample_size < 3 * down_scale_factor:
              raise ValueError(
                  f"""{audio_length_in_s} is too small. Make sure it's bigger or equal to"""
                  f""" {3 * down_scale_factor / self.unet.config.sample_rate}.""" )

          UpperCAmelCase__			:		Optional[Any]													=				int(_A )
          if sample_size % down_scale_factor != 0:
              UpperCAmelCase__			:		List[str]													=				(
                  (audio_length_in_s * self.unet.config.sample_rate) // down_scale_factor + 1
              ) * down_scale_factor
              logger.info(
                  f"""{audio_length_in_s} is increased to {sample_size / self.unet.config.sample_rate} so that it can be handled"""
                  f""" by the model. It will be cut to {original_sample_size / self.unet.config.sample_rate} after the denoising"""
                  ''' process.''' )
          UpperCAmelCase__			:		Union[str, Any]													=				int(_A )

          UpperCAmelCase__			:		Any													=				next(iter(self.unet.parameters() ) ).dtype
          UpperCAmelCase__			:		Union[str, Any]													=				(batch_size, self.unet.config.in_channels, sample_size)
          if isinstance(_A						,						_A ) and len(_A ) != batch_size:
              raise ValueError(
                  f"""You have passed a list of generators of length {len(_A )}, but requested an effective batch"""
                  f""" size of {batch_size}. Make sure the batch size matches the length of the generators.""" )

          UpperCAmelCase__			:		int													=				randn_tensor(_A						,						generator=_A						,						device=self.device						,						dtype=_A )

          # set step values
          self.scheduler.set_timesteps(_A						,						device=audio.device )
          UpperCAmelCase__			:		Union[str, Any]													=				self.scheduler.timesteps.to(_A )

          for t in self.progress_bar(self.scheduler.timesteps ):
              # 1. predict noise model_output
              UpperCAmelCase__			:		Any													=				self.unet(_A						,						_A ).sample

              # 2. compute previous image: x_t -> t_t-1
              UpperCAmelCase__			:		Union[str, Any]													=				self.scheduler.step(_A						,						_A						,						_A ).prev_sample

          UpperCAmelCase__			:		Any													=				audio.clamp(-1						,						1 ).float().cpu().numpy()

          UpperCAmelCase__			:		List[str]													=				audio[:, :, :original_sample_size]

          if not return_dict:
              return (audio,)

          return AudioPipelineOutput(audios=_A )
