


'''simple docstring'''


# DISCLAIMER: This file is strongly influenced by https://github.com/yang-song/score_sde_pytorch

import math
from typing import Union

import torch

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



class 	__lowerCAmelCase		(							__SCREAMING_SNAKE_CASE  , __SCREAMING_SNAKE_CASE    ):


  '''simple docstring'''







  a_  					=							1






  @register_to_config
  def __init__(							self :       str	,_a :       Dict=2000	,_a :       Optional[Any]=0.1	,_a :       List[str]=20	,_a :       Tuple=1e-3 ):

        '''simple docstring'''




        A_						:  List[str]          =				None
        A_						:  Tuple          =				None
        A_						:  Any          =				None






  def        _a							(							self :       int	,_a :       Optional[int]	,_a :       Union[str, torch.device] = None ):

        '''simple docstring'''




        A_						:  int          =				torch.linspace(1	,self.config.sampling_eps	,_a	,device=_a )






  def        _a							(							self :       int	,_a :       str	,_a :       Optional[int]	,_a :       str	,_a :       List[Any]=None ):

        '''simple docstring'''




        if self.timesteps is None:
              raise ValueError(
                  """`self.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler""" )

        # TODO(Patrick) better comments + non-PyTorch
        # postprocess model score
        A_						:  str          =				(
            -0.25 * t**2 * (self.config.beta_max - self.config.beta_min) - 0.5 * t * self.config.beta_min
        )
        A_						:  Union[str, Any]          =				torch.sqrt(1.0 - torch.exp(2.0 * log_mean_coeff ) )
        A_						:  Any          =				std.flatten()
        while len(std.shape ) < len(score.shape ):
              A_						:  List[str]          =				std.unsqueeze(-1 )
        A_						:  Dict          =				-score / std

        # compute
        A_						:  Dict          =				-1.0 / len(self.timesteps )

        A_						:  Optional[int]          =				self.config.beta_min + t * (self.config.beta_max - self.config.beta_min)
        A_						:  Optional[int]          =				beta_t.flatten()
        while len(beta_t.shape ) < len(x.shape ):
              A_						:  str          =				beta_t.unsqueeze(-1 )
        A_						:  int          =				-0.5 * beta_t * x

        A_						:  List[str]          =				torch.sqrt(_a )
        A_						:  Any          =				drift - diffusion**2 * score
        A_						:  Optional[int]          =				x + drift * dt

        # add noise
        A_						:  Optional[Any]          =				randn_tensor(x.shape	,layout=x.layout	,generator=_a	,device=x.device	,dtype=x.dtype )
        A_						:  Dict          =				x_mean + diffusion * math.sqrt(-dt ) * noise

        return x, x_mean






  def __len__(							self :       List[Any] ):

        '''simple docstring'''




        return self.config.num_train_timesteps




'''simple docstring'''


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




def      lowerCamelCase					(      lowerCamelCase  :      str							,						lowerCamelCase  :      complex							,						lowerCamelCase  :      str = "x"							,						lowerCamelCase  :      float = 10**-10							,						lowerCamelCase  :      int = 1							,						):
      A_						:  int          =				symbols(lowerCamelCase)
      A_						:  List[Any]          =				lambdify(lowerCamelCase							,						lowerCamelCase)
      A_						:  List[str]          =				lambdify(lowerCamelCase							,						diff(lowerCamelCase							,						lowerCamelCase))

      A_						:  str          =				starting_point

      while True:
            if diff_function(lowerCamelCase) != 0:
                  A_						:  int          =				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

            A_						:  Union[str, Any]          =				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_0_5)}""",
     )

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