"""simple docstring"""




import math
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 KarrasDiffusionSchedulers, SchedulerMixin


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

@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerDiscrete
class        __SCREAMING_SNAKE_CASE     (   _lowerCAmelCase							):
				UpperCAmelCase	=      42
				UpperCAmelCase	=      None





def 				__a       (			_lowercase							, _lowercase=0.999							, _lowercase="cosine"							, ):







					"""simple docstring"""





					if alpha_transform_type == "cosine":

										def alpha_bar_fn(_lowercase						):
															return math.cos((t + 0.008) / 1.008 * math.pi / 2						) ** 2

					elif alpha_transform_type == "exp":

										def alpha_bar_fn(_lowercase						):
															return math.exp(t * -12.0						)

					else:
										raise ValueError(f"""Unsupported alpha_tranform_type: {alpha_transform_type}"""						)

					lowerCamelCase__		:   int  				=					[]
					for i in range(_lowercase						):
										lowerCamelCase__		:   str  				=					i / num_diffusion_timesteps
										lowerCamelCase__		:   int  				=					(i + 1) / num_diffusion_timesteps
										betas.append(min(1 - alpha_bar_fn(_lowercase						) / alpha_bar_fn(_lowercase						)							, _lowercase						)						)
					return torch.tensor(_lowercase							, dtype=torch.floataa						)





class        __SCREAMING_SNAKE_CASE     (   _lowerCAmelCase						,       _lowerCAmelCase							):
				UpperCAmelCase	=      [e.name for e in KarrasDiffusionSchedulers]
				UpperCAmelCase	=      1







				@register_to_config
				def __init__(    self    :List[Any]      ,__UpperCAmelCase    :int = 10_00      ,__UpperCAmelCase    :float = 0.0_001      ,__UpperCAmelCase    :float = 0.02      ,__UpperCAmelCase    :str = "linear"      ,__UpperCAmelCase    :Optional[Union[np.ndarray, List[float]]] = None      ,__UpperCAmelCase    :str = "epsilon"      ,__UpperCAmelCase    :str = "linear"      ,__UpperCAmelCase    :Optional[bool] = False      ,__UpperCAmelCase    :str = "linspace"      ,__UpperCAmelCase    :int = 0      ,)      ->					Tuple:




									"""simple docstring"""



									if trained_betas is not None:
														lowerCamelCase__		:   List[str]  				=					torch.tensor(__UpperCAmelCase      ,dtype=torch.floataa  )
									elif beta_schedule == "linear":
														lowerCamelCase__		:   Optional[int]  				=					torch.linspace(__UpperCAmelCase      ,__UpperCAmelCase      ,__UpperCAmelCase      ,dtype=torch.floataa  )
									elif beta_schedule == "scaled_linear":
														# this schedule is very specific to the latent diffusion model.
														lowerCamelCase__		:   Dict  				=					(
														    torch.linspace(beta_start**0.5      ,beta_end**0.5      ,__UpperCAmelCase      ,dtype=torch.floataa  ) ** 2
														)
									elif beta_schedule == "squaredcos_cap_v2":
														# Glide cosine schedule
														lowerCamelCase__		:   Tuple  				=					betas_for_alpha_bar(__UpperCAmelCase  )
									else:
														raise NotImplementedError(F"""{beta_schedule} does is not implemented for {self.__class__}"""  )

									lowerCamelCase__		:   str  				=					1.0 - self.betas
									lowerCamelCase__		:   Optional[int]  				=					torch.cumprod(self.alphas      ,dim=0  )

									lowerCamelCase__		:   Union[str, Any]  				=					np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5  )
									lowerCamelCase__		:   Union[str, Any]  				=					np.concatenate([sigmas[::-1], [0.0]]  ).astype(np.floataa  )
									lowerCamelCase__		:   Any  				=					torch.from_numpy(__UpperCAmelCase  )

									# setable values
									lowerCamelCase__		:   Optional[int]  				=					None
									lowerCamelCase__		:   str  				=					np.linspace(0      ,num_train_timesteps - 1      ,__UpperCAmelCase      ,dtype=__UpperCAmelCase  )[::-1].copy()
									lowerCamelCase__		:   int  				=					torch.from_numpy(__UpperCAmelCase  )
									lowerCamelCase__		:   Union[str, Any]  				=					False
									lowerCamelCase__		:   Any  				=					use_karras_sigmas







				@property
				def   lowercase_		(    self    :Any  )      ->					Dict:




									"""simple docstring"""



									if self.config.timestep_spacing in ["linspace", "trailing"]:
														return self.sigmas.max()

									return (self.sigmas.max() ** 2 + 1) ** 0.5







				def   lowercase_		(    self    :Any      ,__UpperCAmelCase    :torch.FloatTensor      ,__UpperCAmelCase    :Union[float, torch.FloatTensor]  )      ->					torch.FloatTensor:




									"""simple docstring"""



									if isinstance(__UpperCAmelCase      ,torch.Tensor  ):
														lowerCamelCase__		:   int  				=					timestep.to(self.timesteps.device  )
									lowerCamelCase__		:   Dict  				=					(self.timesteps == timestep).nonzero().item()
									lowerCamelCase__		:   Union[str, Any]  				=					self.sigmas[step_index]

									lowerCamelCase__		:   int  				=					sample / ((sigma**2 + 1) ** 0.5)

									lowerCamelCase__		:   List[str]  				=					True
									return sample







				def   lowercase_		(    self    :str      ,__UpperCAmelCase    :int      ,__UpperCAmelCase    :Union[str, torch.device] = None  )      ->					str:




									"""simple docstring"""



									lowerCamelCase__		:   Union[str, Any]  				=					num_inference_steps

									# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
									if self.config.timestep_spacing == "linspace":
														lowerCamelCase__		:   Dict  				=					np.linspace(0      ,self.config.num_train_timesteps - 1      ,__UpperCAmelCase      ,dtype=__UpperCAmelCase  )[
														    ::-1
														].copy()
									elif self.config.timestep_spacing == "leading":
														lowerCamelCase__		:   str  				=					self.config.num_train_timesteps // self.num_inference_steps
														# creates integer timesteps by multiplying by ratio
														# casting to int to avoid issues when num_inference_step is power of 3
														lowerCamelCase__		:   Optional[Any]  				=					(np.arange(0      ,__UpperCAmelCase  ) * step_ratio).round()[::-1].copy().astype(__UpperCAmelCase  )
														timesteps += self.config.steps_offset
									elif self.config.timestep_spacing == "trailing":
														lowerCamelCase__		:   Optional[int]  				=					self.config.num_train_timesteps / self.num_inference_steps
														# creates integer timesteps by multiplying by ratio
														# casting to int to avoid issues when num_inference_step is power of 3
														lowerCamelCase__		:   Tuple  				=					(np.arange(self.config.num_train_timesteps      ,0      ,-step_ratio  )).round().copy().astype(__UpperCAmelCase  )
														timesteps -= 1
									else:
														raise ValueError(
														    F"""{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'."""  )

									lowerCamelCase__		:   List[str]  				=					np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5  )
									lowerCamelCase__		:   int  				=					np.log(__UpperCAmelCase  )

									if self.config.interpolation_type == "linear":
														lowerCamelCase__		:   Optional[int]  				=					np.interp(__UpperCAmelCase      ,np.arange(0      ,len(__UpperCAmelCase  )  )      ,__UpperCAmelCase  )
									elif self.config.interpolation_type == "log_linear":
														lowerCamelCase__		:   Dict  				=					torch.linspace(np.log(sigmas[-1]  )      ,np.log(sigmas[0]  )      ,num_inference_steps + 1  ).exp()
									else:
														raise ValueError(
														    F"""{self.config.interpolation_type} is not implemented. Please specify interpolation_type to either"""
														    ''' \'linear\' or \'log_linear\''''  )

									if self.use_karras_sigmas:
														lowerCamelCase__		:   Union[str, Any]  				=					self._convert_to_karras(in_sigmas=__UpperCAmelCase      ,num_inference_steps=self.num_inference_steps  )
														lowerCamelCase__		:   Union[str, Any]  				=					np.array([self._sigma_to_t(__UpperCAmelCase      ,__UpperCAmelCase  ) for sigma in sigmas]  )

									lowerCamelCase__		:   List[str]  				=					np.concatenate([sigmas, [0.0]]  ).astype(np.floataa  )
									lowerCamelCase__		:   str  				=					torch.from_numpy(__UpperCAmelCase  ).to(device=__UpperCAmelCase  )
									if str(__UpperCAmelCase  ).startswith('''mps'''  ):
														# mps does not support float64
														lowerCamelCase__		:   List[str]  				=					torch.from_numpy(__UpperCAmelCase  ).to(__UpperCAmelCase      ,dtype=torch.floataa  )
									else:
														lowerCamelCase__		:   Any  				=					torch.from_numpy(__UpperCAmelCase  ).to(device=__UpperCAmelCase  )







				def   lowercase_		(    self    :Tuple      ,__UpperCAmelCase    :Any      ,__UpperCAmelCase    :Optional[int]  )      ->					Union[str, Any]:




									"""simple docstring"""



									lowerCamelCase__		:   Tuple  				=					np.log(__UpperCAmelCase  )

									# get distribution
									lowerCamelCase__		:   Any  				=					log_sigma - log_sigmas[:, np.newaxis]

									# get sigmas range
									lowerCamelCase__		:   List[Any]  				=					np.cumsum((dists >= 0)      ,axis=0  ).argmax(axis=0  ).clip(max=log_sigmas.shape[0] - 2  )
									lowerCamelCase__		:   List[str]  				=					low_idx + 1

									lowerCamelCase__		:   Union[str, Any]  				=					log_sigmas[low_idx]
									lowerCamelCase__		:   Tuple  				=					log_sigmas[high_idx]

									# interpolate sigmas
									lowerCamelCase__		:   str  				=					(low - log_sigma) / (low - high)
									lowerCamelCase__		:   int  				=					np.clip(__UpperCAmelCase      ,0      ,1  )

									# transform interpolation to time range
									lowerCamelCase__		:   Any  				=					(1 - w) * low_idx + w * high_idx
									lowerCamelCase__		:   Optional[Any]  				=					t.reshape(sigma.shape  )
									return t







				def   lowercase_		(    self    :Any      ,__UpperCAmelCase    :torch.FloatTensor      ,__UpperCAmelCase    :str  )      ->					torch.FloatTensor:




									"""simple docstring"""



									lowerCamelCase__		:   float  				=					in_sigmas[-1].item()
									lowerCamelCase__		:   float  				=					in_sigmas[0].item()

									lowerCamelCase__		:   int  				=					7.0  # 7.0 is the value used in the paper
									lowerCamelCase__		:   Any  				=					np.linspace(0      ,1      ,__UpperCAmelCase  )
									lowerCamelCase__		:   Union[str, Any]  				=					sigma_min ** (1 / rho)
									lowerCamelCase__		:   int  				=					sigma_max ** (1 / rho)
									lowerCamelCase__		:   Dict  				=					(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
									return sigmas







				def   lowercase_		(    self    :List[str]      ,__UpperCAmelCase    :torch.FloatTensor      ,__UpperCAmelCase    :Union[float, torch.FloatTensor]      ,__UpperCAmelCase    :torch.FloatTensor      ,__UpperCAmelCase    :float = 0.0      ,__UpperCAmelCase    :float = 0.0      ,__UpperCAmelCase    :float = float('''inf'''  )      ,__UpperCAmelCase    :float = 1.0      ,__UpperCAmelCase    :Optional[torch.Generator] = None      ,__UpperCAmelCase    :bool = True      ,)      ->					Union[EulerDiscreteSchedulerOutput, Tuple]:




									"""simple docstring"""



									if (
									    isinstance(__UpperCAmelCase      ,__UpperCAmelCase  )
									    or isinstance(__UpperCAmelCase      ,torch.IntTensor  )
									    or isinstance(__UpperCAmelCase      ,torch.LongTensor  )
									):
														raise ValueError(
														    (
														        '''Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to'''
														        ''' `EulerDiscreteScheduler.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(__UpperCAmelCase      ,torch.Tensor  ):
														lowerCamelCase__		:   List[Any]  				=					timestep.to(self.timesteps.device  )

									lowerCamelCase__		:   str  				=					(self.timesteps == timestep).nonzero().item()
									lowerCamelCase__		:   Optional[Any]  				=					self.sigmas[step_index]

									lowerCamelCase__		:   str  				=					min(s_churn / (len(self.sigmas  ) - 1)      ,2**0.5 - 1  ) if s_tmin <= sigma <= s_tmax else 0.0

									lowerCamelCase__		:   List[str]  				=					randn_tensor(
									    model_output.shape      ,dtype=model_output.dtype      ,device=model_output.device      ,generator=__UpperCAmelCase  )

									lowerCamelCase__		:   Any  				=					noise * s_noise
									lowerCamelCase__		:   Tuple  				=					sigma * (gamma + 1)

									if gamma > 0:
														lowerCamelCase__		:   Union[str, Any]  				=					sample + eps * (sigma_hat**2 - sigma**2) ** 0.5

									# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
									# NOTE: "original_sample" should not be an expected prediction_type but is left in for
									# backwards compatibility
									if self.config.prediction_type == "original_sample" or self.config.prediction_type == "sample":
														lowerCamelCase__		:   List[Any]  				=					model_output
									elif self.config.prediction_type == "epsilon":
														lowerCamelCase__		:   Tuple  				=					sample - sigma_hat * model_output
									elif self.config.prediction_type == "v_prediction":
														# * c_out + input * c_skip
														lowerCamelCase__		:   Any  				=					model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
									else:
														raise ValueError(
														    F"""prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"""  )

									# 2. Convert to an ODE derivative
									lowerCamelCase__		:   str  				=					(sample - pred_original_sample) / sigma_hat

									lowerCamelCase__		:   Union[str, Any]  				=					self.sigmas[step_index + 1] - sigma_hat

									lowerCamelCase__		:   List[Any]  				=					sample + derivative * dt

									if not return_dict:
														return (prev_sample,)

									return EulerDiscreteSchedulerOutput(prev_sample=__UpperCAmelCase      ,pred_original_sample=__UpperCAmelCase  )







				def   lowercase_		(    self    :Any      ,__UpperCAmelCase    :torch.FloatTensor      ,__UpperCAmelCase    :torch.FloatTensor      ,__UpperCAmelCase    :torch.FloatTensor      ,)      ->					torch.FloatTensor:




									"""simple docstring"""



									lowerCamelCase__		:   List[Any]  				=					self.sigmas.to(device=original_samples.device      ,dtype=original_samples.dtype  )
									if original_samples.device.type == "mps" and torch.is_floating_point(__UpperCAmelCase  ):
														# mps does not support float64
														lowerCamelCase__		:   str  				=					self.timesteps.to(original_samples.device      ,dtype=torch.floataa  )
														lowerCamelCase__		:   int  				=					timesteps.to(original_samples.device      ,dtype=torch.floataa  )
									else:
														lowerCamelCase__		:   Union[str, Any]  				=					self.timesteps.to(original_samples.device  )
														lowerCamelCase__		:   str  				=					timesteps.to(original_samples.device  )

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

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

									lowerCamelCase__		:   Optional[Any]  				=					original_samples + noise * sigma
									return noisy_samples







				def __len__(    self    :int  )      ->					Any:




									"""simple docstring"""



									return self.config.num_train_timesteps







"""simple docstring"""




from collections.abc import Callable

UpperCAmelCase       :    Optional[int]									=			Callable[[float], float]  # type alias for a real -> real function



def 				__a       (			_lowercase							, _lowercase							, _lowercase							, ):







					"""simple docstring"""





					lowerCamelCase__		:   Tuple  				=					float(_lowercase						)
					while True:
										try:
															lowerCamelCase__		:   str  				=					prev_guess - function(_lowercase						) / derivative(_lowercase						)
										except ZeroDivisionError:
															raise ZeroDivisionError('''Could not find root'''						) from None
										if abs(prev_guess - next_guess						) < 10**-5:
															return next_guess
										lowerCamelCase__		:   List[str]  				=					next_guess



def 				__a       (			_lowercase						):







					"""simple docstring"""





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



def 				__a       (			_lowercase						):







					"""simple docstring"""





					return 3 * (x**2) - 2


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






