
import math as m







def snake_case_    (				lowercase__      ,					lowercase__      ,					lowercase__=0.001		):
  return (f(a + h		) - f(a - h		)) / (2 * h)







def snake_case_    (				lowercase__      ,					lowercase__=0      ,					lowercase__=1_0_0      ,					lowercase__=0.0001      ,					lowercase__=1E-6      ,					lowercase__=False		):
  UpperCAmelCase__			:				Dict												=       xa  # set the initial guess
  UpperCAmelCase__			:				Tuple												=       [a]
  UpperCAmelCase__			:				List[str]												=       abs(f(lowercase__		)		)
  UpperCAmelCase__			:				Any												=       lambda lowercase__		: calc_derivative(lowercase__      ,					lowercase__      ,					h=lowercase__		)  # noqa: E731  Derivative of f(x)
  for _ in range(lowercase__		):
    if fa(lowercase__		) == 0:
      raise ValueError("No converging solution found"		)
    UpperCAmelCase__			:				Union[str, Any]												=       a - f(lowercase__		) / fa(lowercase__		)  # Calculate the next estimate
    if logsteps:
      steps.append(lowercase__		)
    if error < maxerror:
      break
  else:
    raise ValueError("Iteration limit reached, no converging solution found"		)
  if logsteps:
    # If logstep is true, then log intermediate steps
    return a, error, steps
  return a, error


if __name__ == "__main__":
      from matplotlib import pyplot as plt

      SCREAMING_SNAKE_CASE    =					lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
      SCREAMING_SNAKE_CASE,	SCREAMING_SNAKE_CASE,	SCREAMING_SNAKE_CASE    =					newton_raphson(
          f, xa=1_0, maxiter=1_0_0_0, step=1E-6, logsteps=True
      )
      plt.plot([abs(f(x)) for x in steps])
      plt.xlabel("""step""")
      plt.ylabel("""error""")
      plt.show()
      print(F'solution = {{{solution:f}}}, error = {{{error:f}}}')





'''simple docstring'''





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

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

import flax
import jax.numpy as jnp
from jax import random

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import FlaxSchedulerMixin, FlaxSchedulerOutput, broadcast_to_shape_from_left






@flax.struct.dataclass
class        UpperCAmelCase_       :

 '''simple docstring'''
 # setable values
 lowercase_				:						Optional[jnp.ndarray]				=       None
 lowercase_				:						Optional[jnp.ndarray]				=       None
 lowercase_				:						Optional[jnp.ndarray]				=       None







 @classmethod
 def        UpperCamelCase     (				cls		:     List[str]   ):



   '''simple docstring'''




   return cls()






@dataclass
class        UpperCAmelCase_       (						A							):

 '''simple docstring'''
 lowercase_				:						ScoreSdeVeSchedulerState
 lowercase_				:						jnp.ndarray
 lowercase_				:						Optional[jnp.ndarray]				=       None






class        UpperCAmelCase_       (						A				,							A							):

 '''simple docstring'''







 @property
 def        UpperCamelCase     (				self		:     List[Any]   ):



   '''simple docstring'''




   return True







 @register_to_config
 def __init__(				self		:     Optional[Any] ,							snake_case__		:     int = 20_00 ,							snake_case__		:     float = 0.15 ,							snake_case__		:     float = 0.01 ,							snake_case__		:     float = 1348.0 ,							snake_case__		:     float = 1e-5 ,							snake_case__		:     int = 1 ,							):



   '''simple docstring'''




   pass







 def        UpperCamelCase     (				self		:     Optional[int]   ):



   '''simple docstring'''




   UpperCAmelCase__			:				Union[str, Any]												=       ScoreSdeVeSchedulerState.create()
   return self.set_sigmas(
       snake_case__ ,							self.config.num_train_timesteps ,							self.config.sigma_min ,							self.config.sigma_max ,							self.config.sampling_eps ,							)







 def        UpperCamelCase     (				self		:     List[Any] ,							snake_case__		:     ScoreSdeVeSchedulerState ,							snake_case__		:     int ,							snake_case__		:     Tuple = () ,							snake_case__		:     float = None   ):



   '''simple docstring'''




   UpperCAmelCase__			:				str												=       sampling_eps if sampling_eps is not None else self.config.sampling_eps

   UpperCAmelCase__			:				Optional[int]												=       jnp.linspace(1 ,							snake_case__ ,							snake_case__   )
   return state.replace(timesteps=snake_case__   )







 def        UpperCamelCase     (				self		:     str ,							snake_case__		:     ScoreSdeVeSchedulerState ,							snake_case__		:     int ,							snake_case__		:     float = None ,							snake_case__		:     float = None ,							snake_case__		:     float = None ,							):



   '''simple docstring'''




   UpperCAmelCase__			:				int												=       sigma_min if sigma_min is not None else self.config.sigma_min
   UpperCAmelCase__			:				Dict												=       sigma_max if sigma_max is not None else self.config.sigma_max
   UpperCAmelCase__			:				Any												=       sampling_eps if sampling_eps is not None else self.config.sampling_eps
   if state.timesteps is None:
     UpperCAmelCase__			:				Optional[int]												=       self.set_timesteps(snake_case__ ,							snake_case__ ,							snake_case__   )

   UpperCAmelCase__			:				int												=       jnp.exp(jnp.linspace(jnp.log(snake_case__   ) ,							jnp.log(snake_case__   ) ,							snake_case__   )   )
   UpperCAmelCase__			:				Optional[int]												=       jnp.array([sigma_min * (sigma_max / sigma_min) ** t for t in state.timesteps]   )

   return state.replace(discrete_sigmas=snake_case__ ,							sigmas=snake_case__   )







 def        UpperCamelCase     (				self		:     List[str] ,							snake_case__		:     str ,							snake_case__		:     Tuple ,							snake_case__		:     Dict   ):



   '''simple docstring'''




   return jnp.where(timesteps == 0 ,							jnp.zeros_like(snake_case__   ) ,							state.discrete_sigmas[timesteps - 1]   )







 def        UpperCamelCase     (				self		:     Optional[int] ,							snake_case__		:     ScoreSdeVeSchedulerState ,							snake_case__		:     jnp.ndarray ,							snake_case__		:     int ,							snake_case__		:     jnp.ndarray ,							snake_case__		:     random.KeyArray ,							snake_case__		:     bool = True ,							):



   '''simple docstring'''




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

   UpperCAmelCase__			:				str												=       timestep * jnp.ones(
       sample.shape[0] ,							)
   UpperCAmelCase__			:				int												=       (timestep * (len(state.timesteps   ) - 1)).long()

   UpperCAmelCase__			:				Optional[int]												=       state.discrete_sigmas[timesteps]
   UpperCAmelCase__			:				str												=       self.get_adjacent_sigma(snake_case__ ,							snake_case__ ,							snake_case__   )
   UpperCAmelCase__			:				Optional[Any]												=       jnp.zeros_like(snake_case__   )
   UpperCAmelCase__			:				List[Any]												=       (sigma**2 - adjacent_sigma**2) ** 0.5

   # equation 6 in the paper: the model_output modeled by the network is grad_x log pt(x)
   # also equation 47 shows the analog from SDE models to ancestral sampling methods
   UpperCAmelCase__			:				Optional[Any]												=       diffusion.flatten()
   UpperCAmelCase__			:				List[str]												=       broadcast_to_shape_from_left(snake_case__ ,							sample.shape   )
   UpperCAmelCase__			:				Optional[Any]												=       drift - diffusion**2 * model_output

   #  equation 6: sample noise for the diffusion term of
   UpperCAmelCase__			:				List[str]												=       random.split(snake_case__ ,							num=1   )
   UpperCAmelCase__			:				Dict												=       random.normal(key=snake_case__ ,							shape=sample.shape   )
   UpperCAmelCase__			:				Optional[int]												=       sample - drift  # subtract because `dt` is a small negative timestep
   # TODO is the variable diffusion the correct scaling term for the noise?
   UpperCAmelCase__			:				int												=       prev_sample_mean + diffusion * noise  # add impact of diffusion field g

   if not return_dict:
     return (prev_sample, prev_sample_mean, state)

   return FlaxSdeVeOutput(prev_sample=snake_case__ ,							prev_sample_mean=snake_case__ ,							state=snake_case__   )







 def        UpperCamelCase     (				self		:     Any ,							snake_case__		:     ScoreSdeVeSchedulerState ,							snake_case__		:     jnp.ndarray ,							snake_case__		:     jnp.ndarray ,							snake_case__		:     random.KeyArray ,							snake_case__		:     bool = True ,							):



   '''simple docstring'''




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

   # For small batch sizes, the paper "suggest replacing norm(z) with sqrt(d), where d is the dim. of z"
   # sample noise for correction
   UpperCAmelCase__			:				str												=       random.split(snake_case__ ,							num=1   )
   UpperCAmelCase__			:				Tuple												=       random.normal(key=snake_case__ ,							shape=sample.shape   )

   # compute step size from the model_output, the noise, and the snr
   UpperCAmelCase__			:				Union[str, Any]												=       jnp.linalg.norm(snake_case__   )
   UpperCAmelCase__			:				List[str]												=       jnp.linalg.norm(snake_case__   )
   UpperCAmelCase__			:				Optional[Any]												=       (self.config.snr * noise_norm / grad_norm) ** 2 * 2
   UpperCAmelCase__			:				str												=       step_size * jnp.ones(sample.shape[0]   )

   # compute corrected sample: model_output term and noise term
   UpperCAmelCase__			:				Union[str, Any]												=       step_size.flatten()
   UpperCAmelCase__			:				Optional[int]												=       broadcast_to_shape_from_left(snake_case__ ,							sample.shape   )
   UpperCAmelCase__			:				Tuple												=       sample + step_size * model_output
   UpperCAmelCase__			:				Any												=       prev_sample_mean + ((step_size * 2) ** 0.5) * noise

   if not return_dict:
     return (prev_sample, state)

   return FlaxSdeVeOutput(prev_sample=snake_case__ ,							state=snake_case__   )







 def __len__(				self		:     List[str]   ):



   '''simple docstring'''




   return self.config.num_train_timesteps



