



# DISCLAIMER: This code is strongly influenced by https://github.com/pesser/pytorch_diffusion
# and https://github.com/hojonathanho/diffusion
import math
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from diffusers.configuration_utils import ConfigMixin, register_to_config
from diffusers.schedulers.scheduling_utils import SchedulerMixin
from diffusers.utils import BaseOutput, deprecate







@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->DDIM
class     __lowerCAmelCase					(    A		):
			UpperCamelCase           =  42
			UpperCamelCase           =  None





def 							A			(  _UpperCAmelCase       :     str							,     _UpperCAmelCase       :     Dict=0.999							,     _UpperCAmelCase       :     Any="cosine"							,     )       ->				Optional[int]:







			'''simple docstring'''
			if alpha_transform_type == "cosine":

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

			elif alpha_transform_type == "exp":

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

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

			_UpperCAmelCase	 =     []
			for i in range(_UpperCAmelCase					):
						_UpperCAmelCase	 =     i / num_diffusion_timesteps
						_UpperCAmelCase	 =     (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		):
			UpperCamelCase           =  1



			@register_to_config
			def __init__(		self     :						Union[str, Any]				,	A     :						int = 10_00				,	A     :						float = 0.0_0_0_1				,	A     :						float = 0.0_2				,	A     :						str = "linear"				,	A     :						Optional[Union[np.ndarray, List[float]]] = None				,	A     :						bool = True				,	A     :						bool = True				,	A     :						int = 0				,	A     :						str = "epsilon"				,	A     :						float = 1.0				,	**A     :						List[Any]				,	)     ->					str:



						"""simple docstring"""






						if kwargs.get('set_alpha_to_one'				,	A) is not None:
									_UpperCAmelCase	 =     (
									    'The `set_alpha_to_one` argument is deprecated. Please use `set_alpha_to_zero` instead.'
									)
									deprecate('set_alpha_to_one'				,	'1.0.0'				,	A				,	standard_warn=A)
									_UpperCAmelCase	 =     kwargs['set_alpha_to_one']
						if trained_betas is not None:
									_UpperCAmelCase	 =     torch.tensor(A				,	dtype=torch.floataa)
						elif beta_schedule == "linear":
									_UpperCAmelCase	 =     torch.linspace(A				,	A				,	A				,	dtype=torch.floataa)
						elif beta_schedule == "scaled_linear":
									# this schedule is very specific to the latent diffusion model.
									_UpperCAmelCase	 =     (
									    torch.linspace(beta_start**0.5				,	beta_end**0.5				,	A				,	dtype=torch.floataa) ** 2
									)
						elif beta_schedule == "squaredcos_cap_v2":
									# Glide cosine schedule
									_UpperCAmelCase	 =     betas_for_alpha_bar(A)
						else:
									raise NotImplementedError(F"{beta_schedule} does is not implemented for {self.__class__}")

						_UpperCAmelCase	 =     1.0 - self.betas
						_UpperCAmelCase	 =     torch.cumprod(self.alphas				,	dim=0)

						# At every step in inverted ddim, we are looking into the next alphas_cumprod
						# For the final step, there is no next alphas_cumprod, and the index is out of bounds
						# `set_alpha_to_zero` decides whether we set this parameter simply to zero
						# in this case, self.step() just output the predicted noise
						# or whether we use the final alpha of the "non-previous" one.
						_UpperCAmelCase	 =     torch.tensor(0.0) if set_alpha_to_zero else self.alphas_cumprod[-1]

						# standard deviation of the initial noise distribution
						_UpperCAmelCase	 =     1.0

						# setable values
						_UpperCAmelCase	 =     None
						_UpperCAmelCase	 =     torch.from_numpy(np.arange(0				,	A).copy().astype(np.intaa))



			def 					_lowerCamelCase (		self     :						int				,	A     :						torch.FloatTensor				,	A     :						Optional[int] = None)     ->					torch.FloatTensor:



						"""simple docstring"""






						return sample



			def 					_lowerCamelCase (		self     :						Optional[Any]				,	A     :						int				,	A     :						Union[str, torch.device] = None)     ->					List[Any]:



						"""simple docstring"""






						if num_inference_steps > self.config.num_train_timesteps:
									raise ValueError(
									    F"`num_inference_steps`: {num_inference_steps} cannot be larger than `self.config.train_timesteps`:"
									    F" {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle"
									    F" maximal {self.config.num_train_timesteps} timesteps.")

						_UpperCAmelCase	 =     num_inference_steps
						_UpperCAmelCase	 =     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
						_UpperCAmelCase	 =     (np.arange(0				,	A) * step_ratio).round().copy().astype(np.intaa)
						_UpperCAmelCase	 =     torch.from_numpy(A).to(A)
						self.timesteps += self.config.steps_offset



			def 					_lowerCamelCase (		self     :						str				,	A     :						torch.FloatTensor				,	A     :						int				,	A     :						torch.FloatTensor				,	A     :						float = 0.0				,	A     :						bool = False				,	A     :						Optional[torch.FloatTensor] = None				,	A     :						bool = True				,	)     ->					Union[DDIMSchedulerOutput, Tuple]:



						"""simple docstring"""






						_UpperCAmelCase	 =     timestep + self.config.num_train_timesteps // self.num_inference_steps

						# 2. compute alphas, betas
						# change original implementation to exactly match noise levels for analogous forward process
						_UpperCAmelCase	 =     self.alphas_cumprod[timestep]
						_UpperCAmelCase	 =     (
						    self.alphas_cumprod[prev_timestep]
						    if prev_timestep < self.config.num_train_timesteps
						    else self.final_alpha_cumprod
						)

						_UpperCAmelCase	 =     1 - alpha_prod_t

						# 3. compute predicted original sample from predicted noise also called
						# "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
						if self.config.prediction_type == "epsilon":
									_UpperCAmelCase	 =     (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
									_UpperCAmelCase	 =     model_output
						elif self.config.prediction_type == "sample":
									_UpperCAmelCase	 =     model_output
									_UpperCAmelCase	 =     (sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5
						elif self.config.prediction_type == "v_prediction":
									_UpperCAmelCase	 =     (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
									_UpperCAmelCase	 =     (alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample
						else:
									raise ValueError(
									    F"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"
									    ' `v_prediction`')

						# 4. Clip or threshold "predicted x_0"
						if self.config.clip_sample:
									_UpperCAmelCase	 =     pred_original_sample.clamp(
									    -self.config.clip_sample_range				,	self.config.clip_sample_range)

						# 5. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
						_UpperCAmelCase	 =     (1 - alpha_prod_t_prev) ** 0.5 * pred_epsilon

						# 6. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
						_UpperCAmelCase	 =     alpha_prod_t_prev ** 0.5 * pred_original_sample + pred_sample_direction

						if not return_dict:
									return (prev_sample, pred_original_sample)
						return DDIMSchedulerOutput(prev_sample=A				,	pred_original_sample=A)



			def __len__(		self     :						int)     ->					Tuple:



						"""simple docstring"""






						return self.config.num_train_timesteps





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





def 							A			(  _UpperCAmelCase       :     str							,     _UpperCAmelCase       :     complex							,     _UpperCAmelCase       :     str = "x"							,     _UpperCAmelCase       :     float = 10**-10							,     _UpperCAmelCase       :     int = 1							,     )       ->				complex:







			'''simple docstring'''
			_UpperCAmelCase	 =     symbols(_UpperCAmelCase					)
			_UpperCAmelCase	 =     lambdify(_UpperCAmelCase							,     _UpperCAmelCase					)
			_UpperCAmelCase	 =     lambdify(_UpperCAmelCase							,     diff(_UpperCAmelCase							,     _UpperCAmelCase					)					)

			_UpperCAmelCase	 =     starting_point

			while True:
						if diff_function(_UpperCAmelCase					) != 0:
									_UpperCAmelCase	 =     prev_guess - multiplicity * func(_UpperCAmelCase					) / diff_function(
									    _UpperCAmelCase					)
						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

						_UpperCAmelCase	 =     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=0.005)}""",
							)

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