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
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->UnCLIP
class    lowercase_  (  lowerCAmelCase__						):



	"""simple docstring"""





	UpperCAmelCase_  :					torch.FloatTensor
	UpperCAmelCase_  :					Optional[torch.FloatTensor]   =				None

def    SCREAMING_SNAKE_CASE_     (						snake_case__   ,  snake_case__=0.9_99   ,  snake_case__="cosine"   ,  )     ->	Dict:
							if alpha_transform_type == "cosine":

														def alpha_bar_fn(snake_case__							):
																					return math.cos((t + 0.0_08) / 1.0_08 * math.pi / 2							) ** 2

							elif alpha_transform_type == "exp":

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

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

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






class    lowercase_  (  lowerCAmelCase__      ,     lowerCAmelCase__						):



	"""simple docstring"""





	@register_to_config
	def __init__(							self		,			__SCREAMING_SNAKE_CASE = 1000		,			__SCREAMING_SNAKE_CASE = "fixed_small_log"		,			__SCREAMING_SNAKE_CASE = True		,			__SCREAMING_SNAKE_CASE = 1.0		,			__SCREAMING_SNAKE_CASE = "epsilon"		,			__SCREAMING_SNAKE_CASE = "squaredcos_cap_v2"		,			)						->Union[str, Any]:
								if beta_schedule != "squaredcos_cap_v2":
															raise ValueError('''UnCLIPScheduler only supports `beta_schedule`: \'squaredcos_cap_v2\''''				)

								lowerCAmelCase			=		betas_for_alpha_bar(lowercase_				)

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

								# standard deviation of the initial noise distribution
								lowerCAmelCase			=		1.0

								# setable values
								lowerCAmelCase			=		None
								lowerCAmelCase			=		torch.from_numpy(np.arange(0		,			lowercase_				)[::-1].copy()				)

								lowerCAmelCase			=		variance_type


	def 			SCREAMING_SNAKE_CASE_				(							self		,			__SCREAMING_SNAKE_CASE		,			__SCREAMING_SNAKE_CASE = None				)						->List[Any]:
								return sample


	def 			SCREAMING_SNAKE_CASE_				(							self		,			__SCREAMING_SNAKE_CASE		,			__SCREAMING_SNAKE_CASE = None				)						->int:
								lowerCAmelCase			=		num_inference_steps
								lowerCAmelCase			=		(self.config.num_train_timesteps - 1) / (self.num_inference_steps - 1)
								lowerCAmelCase			=		(np.arange(0		,			lowercase_				) * step_ratio).round()[::-1].copy().astype(np.intaa				)
								lowerCAmelCase			=		torch.from_numpy(lowercase_				).to(lowercase_				)


	def 			SCREAMING_SNAKE_CASE_				(							self		,			__SCREAMING_SNAKE_CASE		,			__SCREAMING_SNAKE_CASE=None		,			__SCREAMING_SNAKE_CASE=None		,			__SCREAMING_SNAKE_CASE=None				)						->Tuple:
								if prev_timestep is None:
															lowerCAmelCase			=		t - 1

								lowerCAmelCase			=		self.alphas_cumprod[t]
								lowerCAmelCase			=		self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.one
								lowerCAmelCase			=		1 - alpha_prod_t
								lowerCAmelCase			=		1 - alpha_prod_t_prev

								if prev_timestep == t - 1:
															lowerCAmelCase			=		self.betas[t]
								else:
															lowerCAmelCase			=		1 - alpha_prod_t / 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
								lowerCAmelCase			=		beta_prod_t_prev / beta_prod_t * beta

								if variance_type is None:
															lowerCAmelCase			=		self.config.variance_type

								# hacks - were probably added for training stability
								if variance_type == "fixed_small_log":
															lowerCAmelCase			=		torch.log(torch.clamp(lowercase_		,			min=1e-20				)				)
															lowerCAmelCase			=		torch.exp(0.5 * variance				)
								elif variance_type == "learned_range":
															# NOTE difference with DDPM scheduler
															lowerCAmelCase			=		variance.log()
															lowerCAmelCase			=		beta.log()

															lowerCAmelCase			=		(predicted_variance + 1) / 2
															lowerCAmelCase			=		frac * max_log + (1 - frac) * min_log

								return variance


	def 			SCREAMING_SNAKE_CASE_				(							self		,			__SCREAMING_SNAKE_CASE		,			__SCREAMING_SNAKE_CASE		,			__SCREAMING_SNAKE_CASE		,			__SCREAMING_SNAKE_CASE = None		,			__SCREAMING_SNAKE_CASE=None		,			__SCREAMING_SNAKE_CASE = True		,			)						->Dict:
								lowerCAmelCase			=		timestep

								if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type == "learned_range":
															lowerCAmelCase			=		torch.split(lowercase_		,			sample.shape[1]		,			dim=1				)
								else:
															lowerCAmelCase			=		None

								# 1. compute alphas, betas
								if prev_timestep is None:
															lowerCAmelCase			=		t - 1

								lowerCAmelCase			=		self.alphas_cumprod[t]
								lowerCAmelCase			=		self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.one
								lowerCAmelCase			=		1 - alpha_prod_t
								lowerCAmelCase			=		1 - alpha_prod_t_prev

								if prev_timestep == t - 1:
															lowerCAmelCase			=		self.betas[t]
															lowerCAmelCase			=		self.alphas[t]
								else:
															lowerCAmelCase			=		1 - alpha_prod_t / alpha_prod_t_prev
															lowerCAmelCase			=		1 - beta

								# 2. compute predicted original sample from predicted noise also called
								# "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
								if self.config.prediction_type == "epsilon":
															lowerCAmelCase			=		(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
								elif self.config.prediction_type == "sample":
															lowerCAmelCase			=		model_output
								else:
															raise ValueError(
															    F"prediction_type given as {self.config.prediction_type} must be one of `epsilon` or `sample`"
															    ''' for the UnCLIPScheduler.'''				)

								# 3. Clip "predicted x_0"
								if self.config.clip_sample:
															lowerCAmelCase			=		torch.clamp(
															    lowercase_		,			-self.config.clip_sample_range		,			self.config.clip_sample_range				)

								# 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
								# See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
								lowerCAmelCase			=		(alpha_prod_t_prev ** 0.5 * beta) / beta_prod_t
								lowerCAmelCase			=		alpha ** 0.5 * beta_prod_t_prev / beta_prod_t

								# 5. Compute predicted previous sample µ_t
								# See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
								lowerCAmelCase			=		pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

								# 6. Add noise
								lowerCAmelCase			=		0
								if t > 0:
															lowerCAmelCase			=		randn_tensor(
															    model_output.shape		,			dtype=model_output.dtype		,			generator=lowercase_		,			device=model_output.device				)

															lowerCAmelCase			=		self._get_variance(
															    lowercase_		,			predicted_variance=lowercase_		,			prev_timestep=lowercase_		,			)

															if self.variance_type == "fixed_small_log":
																						lowerCAmelCase			=		variance
															elif self.variance_type == "learned_range":
																						lowerCAmelCase			=		(0.5 * variance).exp()
															else:
																						raise ValueError(
																						    F"variance_type given as {self.variance_type} must be one of `fixed_small_log` or `learned_range`"
																						    ''' for the UnCLIPScheduler.'''				)

															lowerCAmelCase			=		variance * variance_noise

								lowerCAmelCase			=		pred_prev_sample + variance

								if not return_dict:
															return (pred_prev_sample,)

								return UnCLIPSchedulerOutput(prev_sample=lowercase_		,			pred_original_sample=lowercase_				)




	def 			SCREAMING_SNAKE_CASE_				(							self		,			__SCREAMING_SNAKE_CASE		,			__SCREAMING_SNAKE_CASE		,			__SCREAMING_SNAKE_CASE		,			)						->Tuple:
								# Make sure alphas_cumprod and timestep have same device and dtype as original_samples
								lowerCAmelCase			=		self.alphas_cumprod.to(device=original_samples.device		,			dtype=original_samples.dtype				)
								lowerCAmelCase			=		timesteps.to(original_samples.device				)

								lowerCAmelCase			=		alphas_cumprod[timesteps] ** 0.5
								lowerCAmelCase			=		sqrt_alpha_prod.flatten()
								while len(sqrt_alpha_prod.shape				) < len(original_samples.shape				):
															lowerCAmelCase			=		sqrt_alpha_prod.unsqueeze(-1				)

								lowerCAmelCase			=		(1 - alphas_cumprod[timesteps]) ** 0.5
								lowerCAmelCase			=		sqrt_one_minus_alpha_prod.flatten()
								while len(sqrt_one_minus_alpha_prod.shape				) < len(original_samples.shape				):
															lowerCAmelCase			=		sqrt_one_minus_alpha_prod.unsqueeze(-1				)

								lowerCAmelCase			=		sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
								return noisy_samples








"""simple docstring"""

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




def __lowercase			(							_a		,			_a		,			_a = "x"		,			_a = 10**-10		,			_a = 1		,			):
    snake_case_ :     Any				=	symbols(_a    )
    snake_case_ :     int				=	lambdify(_a		,			_a    )
    snake_case_ :     Optional[Any]				=	lambdify(_a		,			diff(_a		,			_a    )    )

    snake_case_ :     Optional[Any]				=	starting_point

    while True:
        if diff_function(_a    ) != 0:
            snake_case_ :     Optional[int]				=	prev_guess - multiplicity * func(_a    ) / diff_function(
                _a    )
        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

        snake_case_ :     int				=	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)}')





