code: 
  
  
  
  
  
  
  """simple docstring"""
  
  import math as m
  
  def 	__lowerCamelCase			(						__UpperCamelCase   , __UpperCamelCase   , __UpperCamelCase=0.0_01 )		->					int:
  
  		"""simple docstring"""
  
  
  
  
  
  
  
  		return (f(a + h ) - f(a - h )) / (2 * h)
  
  def 	__lowerCamelCase			(						__UpperCamelCase   , __UpperCamelCase=0   , __UpperCamelCase=100   , __UpperCamelCase=0.00_01   , __UpperCamelCase=1e-6   , __UpperCamelCase=False )		->					Tuple:
  
  		"""simple docstring"""
  
  
  
  
  
  
  
  		lowerCAmelCase_     :							str             =    xa  # set the initial guess
  		lowerCAmelCase_     :							int             =    [a]
  		lowerCAmelCase_     :							Optional[int]             =    abs(f(__UpperCamelCase ) )
  		lowerCAmelCase_     :							List[Any]             =    lambda __UpperCamelCase : calc_derivative(__UpperCamelCase   , __UpperCamelCase   , h=__UpperCamelCase )  # noqa: E731  Derivative of f(x)
  		for _ in range(__UpperCamelCase ):
  				if fa(__UpperCamelCase ) == 0:
  						raise ValueError("No converging solution found" )
  				lowerCAmelCase_     :							Union[str, Any]             =    a - f(__UpperCamelCase ) / fa(__UpperCamelCase )  # Calculate the next estimate
  				if logsteps:
  						steps.append(__UpperCamelCase )
  				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
  
  					lowercase__      =				lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
  					lowercase__ ,     lowercase__ ,     lowercase__      =				newton_raphson(
  					    f, xa=10, maxiter=1000, 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}}}""")
  
style_context: 
  
  
  
  
  
  
  """simple docstring"""
  
  import math
  from dataclasses import dataclass
  from typing import Optional, Tuple, Union
  
  import numpy as np
  import torch
  
  from ..configuration_utils import ConfigMixin, register_to_config
  from ..utils import BaseOutput, randn_tensor
  from .scheduling_utils import SchedulerMixin
  
  
  @dataclass
  class 	__lowerCamelCase       (				A__    ):
  
  
  
  
  
  		'''simple docstring'''
  
  
  
  
  
  
  		a_			:       torch.FloatTensor
  		a_			:       torch.FloatTensor
  
  
  
  
  
  
  
  def 	__lowerCamelCase			(						__UpperCamelCase   , __UpperCamelCase=0.9_99   , __UpperCamelCase="cosine"   , )		->					Any:
  
  		"""simple docstring"""
  
  
  
  
  
  
  
  		if alpha_transform_type == "cosine":
  
  				def alpha_bar_fn(__UpperCamelCase ):
  						return math.cos((t + 0.0_08) / 1.0_08 * math.pi / 2 ) ** 2
  
  		elif alpha_transform_type == "exp":
  
  				def alpha_bar_fn(__UpperCamelCase ):
  						return math.exp(t * -12.0 )
  
  		else:
  				raise ValueError(f'''Unsupported alpha_tranform_type: {alpha_transform_type}''' )
  
  		lowerCAmelCase_     :							List[str]             =    []
  		for i in range(__UpperCamelCase ):
  				lowerCAmelCase_     :							int             =    i / num_diffusion_timesteps
  				lowerCAmelCase_     :							Optional[Any]             =    (i + 1) / num_diffusion_timesteps
  				betas.append(min(1 - alpha_bar_fn(__UpperCamelCase ) / alpha_bar_fn(__UpperCamelCase )   , __UpperCamelCase ) )
  		return torch.tensor(__UpperCamelCase   , dtype=torch.floataa )
  
  
  
  class 	__lowerCamelCase       (				A__				,							A__    ):
  
  
  
  
  
  		'''simple docstring'''
  
  
  
  
  
  
  		a_			:       Tuple      =							1
  
  
  
  
  
  		@register_to_config
  		def __init__(     self							:			Optional[int]		,    a_							:			int = 10_00		,    a_							:			float = 0.0001		,    a_							:			float = 0.02		,    a_							:			str = "linear"		,    a_							:			float = 0.0		,    a_							:			Optional[np.ndarray] = None		,    a_							:			bool = True		,    ):
  				if trained_betas is not None:
  						lowerCAmelCase_     :							Tuple             =    torch.from_numpy(a_			)
  				elif beta_schedule == "linear":
  						lowerCAmelCase_     :							int             =    torch.linspace(a_		,    a_		,    a_		,    dtype=torch.floataa			)
  				elif beta_schedule == "scaled_linear":
  						# this schedule is very specific to the latent diffusion model.
  						lowerCAmelCase_     :							Optional[Any]             =    (
  						    torch.linspace(beta_start**0.5		,    beta_end**0.5		,    a_		,    dtype=torch.floataa			) ** 2
  						)
  				elif beta_schedule == "squaredcos_cap_v2":
  						# Glide cosine schedule
  						lowerCAmelCase_     :							Tuple             =    betas_for_alpha_bar(a_			)
  				elif beta_schedule == "sigmoid":
  						# GeoDiff sigmoid schedule
  						lowerCAmelCase_     :							List[str]             =    torch.linspace(-6		,    6		,    a_			)
  						lowerCAmelCase_     :							int             =    torch.sigmoid(a_			) * (beta_end - beta_start) + beta_start
  				else:
  						raise NotImplementedError(f'''{beta_schedule} does is not implemented for {self.__class__}'''			)
  
  				lowerCAmelCase_     :							Union[str, Any]             =    1.0 - self.betas
  				lowerCAmelCase_     :							Optional[int]             =    torch.cumprod(self.alphas		,    dim=0			)
  				lowerCAmelCase_     :							int             =    torch.tensor(1.0			)
  
  				lowerCAmelCase_     :							int             =    torch.tensor(1.0			)
  
  				# standard deviation of the initial noise distribution
  				lowerCAmelCase_     :							List[str]             =    1.0
  
  				# setable values
  				lowerCAmelCase_     :							Dict             =    None
  				lowerCAmelCase_     :							List[str]             =    torch.from_numpy(np.arange(0		,    a_			)[::-1].copy()			)
  
  				lowerCAmelCase_     :							int             =    eta
  
  
  
  
  
  		def      lowerCamelCase (     self							:			Optional[Any]		,    a_							:			torch.FloatTensor		,    a_							:			Optional[int] = None			):
  				return sample
  
  
  
  
  
  		def      lowerCamelCase (     self							:			Dict		,    a_							:			int		,    a_							:			int = 10		,    a_							:			int = 10		,    a_							:			Union[str, torch.device] = None		,    ):
  				lowerCAmelCase_     :							Union[str, Any]             =    min(self.config.num_train_timesteps		,    a_			)
  				lowerCAmelCase_     :							Dict             =    num_inference_steps
  
  				lowerCAmelCase_     :							List[str]             =    []
  
  				lowerCAmelCase_     :							Dict             =    {}
  				for j in range(0		,    num_inference_steps - jump_length		,    a_			):
  						lowerCAmelCase_     :							Dict             =    jump_n_sample - 1
  
  				lowerCAmelCase_     :							List[Any]             =    num_inference_steps
  				while t >= 1:
  						lowerCAmelCase_     :							int             =    t - 1
  						timesteps.append(a_			)
  
  						if jumps.get(a_		,    0			) > 0:
  								lowerCAmelCase_     :							Optional[int]             =    jumps[t] - 1
  								for _ in range(a_			):
  										lowerCAmelCase_     :							Any             =    t + 1
  										timesteps.append(a_			)
  
  				lowerCAmelCase_     :							List[Any]             =    np.array(a_			) * (self.config.num_train_timesteps // self.num_inference_steps)
  				lowerCAmelCase_     :							int             =    torch.from_numpy(a_			).to(a_			)
  
  
  
  
  
  		def      lowerCamelCase (     self							:			Optional[int]		,    a_							:			Optional[Any]			):
  				lowerCAmelCase_     :							Optional[Any]             =    t - self.config.num_train_timesteps // self.num_inference_steps
  
  				lowerCAmelCase_     :							List[Any]             =    self.alphas_cumprod[t]
  				lowerCAmelCase_     :							Dict             =    self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
  				lowerCAmelCase_     :							List[str]             =    1 - alpha_prod_t
  				lowerCAmelCase_     :							str             =    1 - alpha_prod_t_prev
  
  				# For t > 0, compute predicted variance βt (see formula (6) and (7) from
  				# https://arxiv.org/pdf/2006.11239.pdf) and sample from it to get
  				# previous sample x_{t-1} ~ N(pred_prev_sample, variance) == add
  				# variance to pred_sample
  				# Is equivalent to formula (16) in https://arxiv.org/pdf/2010.02502.pdf
  				# without eta.
  				# variance = (1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * self.betas[t]
  				lowerCAmelCase_     :							Dict             =    (beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)
  
  				return variance
  
  
  
  
  
  		def      lowerCamelCase (     self							:			Optional[Any]		,    a_							:			torch.FloatTensor		,    a_							:			int		,    a_							:			torch.FloatTensor		,    a_							:			torch.FloatTensor		,    a_							:			torch.FloatTensor		,    a_							:			Optional[torch.Generator] = None		,    a_							:			bool = True		,    ):
  				lowerCAmelCase_     :							Any             =    timestep
  				lowerCAmelCase_     :							str             =    timestep - self.config.num_train_timesteps // self.num_inference_steps
  
  				# 1. compute alphas, betas
  				lowerCAmelCase_     :							Any             =    self.alphas_cumprod[t]
  				lowerCAmelCase_     :							List[str]             =    self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
  				lowerCAmelCase_     :							Optional[Any]             =    1 - alpha_prod_t
  
  				# 2. compute predicted original sample from predicted noise also called
  				# "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
  				lowerCAmelCase_     :							List[Any]             =    (sample - beta_prod_t**0.5 * model_output) / alpha_prod_t**0.5
  
  				# 3. Clip "predicted x_0"
  				if self.config.clip_sample:
  						lowerCAmelCase_     :							Optional[int]             =    torch.clamp(a_		,    -1		,    1			)
  
  				# We choose to follow RePaint Algorithm 1 to get x_{t-1}, however we
  				# substitute formula (7) in the algorithm coming from DDPM paper
  				# (formula (4) Algorithm 2 - Sampling) with formula (12) from DDIM paper.
  				# DDIM schedule gives the same results as DDPM with eta = 1.0
  				# Noise is being reused in 7. and 8., but no impact on quality has
  				# been observed.
  
  				# 5. Add noise
  				lowerCAmelCase_     :							Optional[Any]             =    model_output.device
  				lowerCAmelCase_     :							List[str]             =    randn_tensor(model_output.shape		,    generator=a_		,    device=a_		,    dtype=model_output.dtype			)
  				lowerCAmelCase_     :							List[Any]             =    self.eta * self._get_variance(a_			) ** 0.5
  
  				lowerCAmelCase_     :							Optional[int]             =    0
  				if t > 0 and self.eta > 0:
  						lowerCAmelCase_     :							Optional[int]             =    std_dev_t * noise
  
  				# 6. compute "direction pointing to x_t" of formula (12)
  				# from https://arxiv.org/pdf/2010.02502.pdf
  				lowerCAmelCase_     :							Union[str, Any]             =    (1 - alpha_prod_t_prev - std_dev_t**2) ** 0.5 * model_output
  
  				# 7. compute x_{t-1} of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
  				lowerCAmelCase_     :							Dict             =    alpha_prod_t_prev**0.5 * pred_original_sample + pred_sample_direction + variance
  
  				# 8. Algorithm 1 Line 5 https://arxiv.org/pdf/2201.09865.pdf
  				lowerCAmelCase_     :							Union[str, Any]             =    (alpha_prod_t_prev**0.5) * original_image + ((1 - alpha_prod_t_prev) ** 0.5) * noise
  
  				# 9. Algorithm 1 Line 8 https://arxiv.org/pdf/2201.09865.pdf
  				lowerCAmelCase_     :							Tuple             =    mask * prev_known_part + (1.0 - mask) * prev_unknown_part
  
  				if not return_dict:
  						return (
  						    pred_prev_sample,
  						    pred_original_sample,
  						)
  
  				return RePaintSchedulerOutput(prev_sample=a_		,    pred_original_sample=a_			)
  
  
  
  
  
  		def      lowerCamelCase (     self							:			Dict		,    a_							:			Any		,    a_							:			Dict		,    a_							:			Optional[int]=None			):
  				lowerCAmelCase_     :							Dict             =    self.config.num_train_timesteps // self.num_inference_steps
  
  				for i in range(a_			):
  						lowerCAmelCase_     :							Optional[Any]             =    self.betas[timestep + i]
  						if sample.device.type == "mps":
  								# randn does not work reproducibly on mps
  								lowerCAmelCase_     :							str             =    randn_tensor(sample.shape		,    dtype=sample.dtype		,    generator=a_			)
  								lowerCAmelCase_     :							List[str]             =    noise.to(sample.device			)
  						else:
  								lowerCAmelCase_     :							Tuple             =    randn_tensor(sample.shape		,    generator=a_		,    device=sample.device		,    dtype=sample.dtype			)
  
  						# 10. Algorithm 1 Line 10 https://arxiv.org/pdf/2201.09865.pdf
  						lowerCAmelCase_     :							int             =    (1 - beta) ** 0.5 * sample + beta**0.5 * noise
  
  				return sample
  
  
  
  
  
  		def      lowerCamelCase (     self							:			Any		,    a_							:			torch.FloatTensor		,    a_							:			torch.FloatTensor		,    a_							:			torch.IntTensor		,    ):
  				raise NotImplementedError("Use `DDPMScheduler.add_noise()` to train for sampling with RePaint."			)
  
  
  
  
  
  		def __len__(     self							:			Union[str, Any]			):
  				return self.config.num_train_timesteps
  