






"""simple docstring"""
from typing import Optional, Tuple, Union

import torch
from einops import rearrange, reduce

from diffusers import DDIMScheduler, DDPMScheduler, DiffusionPipeline, ImagePipelineOutput, UNetaDConditionModel
from diffusers.schedulers.scheduling_ddim import DDIMSchedulerOutput
from diffusers.schedulers.scheduling_ddpm import DDPMSchedulerOutput


_lowerCAmelCase       =				8






def       __UpperCamelCase						(		snake_case__ , snake_case__=BITS       ):
	A_		:    Union[str, Any]						     = x.device

	A_		:    List[str]						     = (x * 255).int().clamp(0 , 255       )

	A_		:    Optional[Any]						     = 2 ** torch.arange(bits - 1 , -1 , -1 , device=snake_case__       )
	A_		:    Any						     = rearrange(snake_case__ , """d -> d 1 1"""       )
	A_		:    Dict						     = rearrange(snake_case__ , """b c h w -> b c 1 h w"""       )

	A_		:    Optional[int]						     = ((x & mask) != 0).float()
	A_		:    List[Any]						     = rearrange(snake_case__ , """b c d h w -> b (c d) h w"""       )
	A_		:    Optional[Any]						     = bits * 2 - 1
	return bits






def       __UpperCamelCase						(		snake_case__ , snake_case__=BITS       ):
	A_		:    int						     = x.device

	A_		:    Union[str, Any]						     = (x > 0).int()
	A_		:    List[Any]						     = 2 ** torch.arange(bits - 1 , -1 , -1 , device=snake_case__ , dtype=torch.intaa       )

	A_		:    List[Any]						     = rearrange(snake_case__ , """d -> d 1 1"""       )
	A_		:    List[Any]						     = rearrange(snake_case__ , """b (c d) h w -> b c d h w""" , d=8       )
	A_		:    Dict						     = reduce(x * mask , """b c d h w -> b c h w""" , """sum"""       )
	return (dec / 255).clamp(0.0 , 1.0       )






def       __UpperCamelCase						(		self , snake_case__ , snake_case__ , snake_case__ , snake_case__ = 0.0 , snake_case__ = True , snake_case__=None , snake_case__ = True , ):
	if self.num_inference_steps is None:
		raise ValueError(
		    """Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"""       )

	# See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf
	# Ideally, read DDIM paper in-detail understanding

	# Notation (<variable name> -> <name in paper>
	# - pred_noise_t -> e_theta(x_t, t)
	# - pred_original_sample -> f_theta(x_t, t) or x_0
	# - std_dev_t -> sigma_t
	# - eta -> η
	# - pred_sample_direction -> "direction pointing to x_t"
	# - pred_prev_sample -> "x_t-1"

	# 1. get previous step value (=t-1)
	A_		:    Any						     = timestep - self.config.num_train_timesteps // self.num_inference_steps

	# 2. compute alphas, betas
	A_		:    Optional[Any]						     = self.alphas_cumprod[timestep]
	A_		:    List[str]						     = self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod

	A_		:    Dict						     = 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
	A_		:    str						     = (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5

	# 4. Clip "predicted x_0"
	A_		:    Optional[Any]						     = self.bit_scale
	if self.config.clip_sample:
		A_		:    str						     = torch.clamp(snake_case__ , -scale , snake_case__       )

	# 5. compute variance: "sigma_t(η)" -> see formula (16)
	# σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1)
	A_		:    int						     = self._get_variance(snake_case__ , snake_case__       )
	A_		:    Dict						     = eta * variance ** 0.5

	if use_clipped_model_output:
		# the model_output is always re-derived from the clipped x_0 in Glide
		A_		:    Any						     = (sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5

	# 6. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
	A_		:    Tuple						     = (1 - alpha_prod_t_prev - std_dev_t**2) ** 0.5 * model_output

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

	if eta > 0:
		# randn_like does not support generator https://github.com/pytorch/pytorch/issues/27072
		A_		:    int						     = model_output.device if torch.is_tensor(snake_case__       ) else """cpu"""
		A_		:    Union[str, Any]						     = torch.randn(model_output.shape , dtype=model_output.dtype , generator=snake_case__       ).to(snake_case__       )
		A_		:    str						     = self._get_variance(snake_case__ , snake_case__       ) ** 0.5 * eta * noise

		A_		:    Tuple						     = prev_sample + variance

	if not return_dict:
		return (prev_sample,)

	return DDIMSchedulerOutput(prev_sample=snake_case__ , pred_original_sample=snake_case__       )






def       __UpperCamelCase						(		self , snake_case__ , snake_case__ , snake_case__ , snake_case__="epsilon" , snake_case__=None , snake_case__ = True , ):
	A_		:    Any						     = timestep

	if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type in ["learned", "learned_range"]:
		A_     ,  A_		:    List[str]						     = torch.split(snake_case__ , sample.shape[1] , dim=1       )
	else:
		A_		:    Optional[Any]						     = None

	# 1. compute alphas, betas
	A_		:    Optional[Any]						     = self.alphas_cumprod[t]
	A_		:    Dict						     = self.alphas_cumprod[t - 1] if t > 0 else self.one
	A_		:    Dict						     = 1 - alpha_prod_t
	A_		:    List[str]						     = 1 - alpha_prod_t_prev

	# 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 prediction_type == "epsilon":
		A_		:    Optional[int]						     = (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
	elif prediction_type == "sample":
		A_		:    str						     = model_output
	else:
		raise ValueError(F"""Unsupported prediction_type {prediction_type}."""       )

	# 3. Clip "predicted x_0"
	A_		:    int						     = self.bit_scale
	if self.config.clip_sample:
		A_		:    str						     = torch.clamp(snake_case__ , -scale , snake_case__       )

	# 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
	A_		:    List[Any]						     = (alpha_prod_t_prev ** 0.5 * self.betas[t]) / beta_prod_t
	A_		:    List[Any]						     = self.alphas[t] ** 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
	A_		:    Tuple						     = pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

	# 6. Add noise
	A_		:    Dict						     = 0
	if t > 0:
		A_		:    str						     = torch.randn(
		    model_output.size() , dtype=model_output.dtype , layout=model_output.layout , generator=snake_case__       ).to(model_output.device       )
		A_		:    Union[str, Any]						     = (self._get_variance(snake_case__ , predicted_variance=snake_case__       ) ** 0.5) * noise

	A_		:    Union[str, Any]						     = pred_prev_sample + variance

	if not return_dict:
		return (pred_prev_sample,)

	return DDPMSchedulerOutput(prev_sample=snake_case__ , pred_original_sample=snake_case__       )




class   SCREAMING_SNAKE_CASE	(					_SCREAMING_SNAKE_CASE    ):





	"""simple docstring"""




	def __init__(self  ,  lowerCAmelCase_  ,  lowerCAmelCase_  ,  lowerCAmelCase_ = 1.0  ,  ):
		super().__init__()
		A_		:    int						     = bit_scale
		A_		:    Dict						     = (
		    ddim_bit_scheduler_step if isinstance(lowerCAmelCase_  ,  lowerCAmelCase_				) else ddpm_bit_scheduler_step
		)

		self.register_modules(unet=lowerCAmelCase_  ,  scheduler=lowerCAmelCase_				)





	@torch.no_grad()
	def __call__(self  ,  lowerCAmelCase_ = 256  ,  lowerCAmelCase_ = 256  ,  lowerCAmelCase_ = 50  ,  lowerCAmelCase_ = None  ,  lowerCAmelCase_ = 1  ,  lowerCAmelCase_ = "pil"  ,  lowerCAmelCase_ = True  ,  **lowerCAmelCase_  ,  ):
		A_		:    Optional[Any]						     = torch.randn(
		    (batch_size, self.unet.config.in_channels, height, width)  ,  generator=lowerCAmelCase_  ,  )
		A_		:    Optional[Any]						     = decimal_to_bits(lowerCAmelCase_				) * self.bit_scale
		A_		:    Dict						     = latents.to(self.device				)

		self.scheduler.set_timesteps(lowerCAmelCase_				)

		for t in self.progress_bar(self.scheduler.timesteps				):
			# predict the noise residual
			A_		:    int						     = self.unet(lowerCAmelCase_  ,  lowerCAmelCase_				).sample

			# compute the previous noisy sample x_t -> x_t-1
			A_		:    Optional[int]						     = self.scheduler.step(lowerCAmelCase_  ,  lowerCAmelCase_  ,  lowerCAmelCase_				).prev_sample

		A_		:    Tuple						     = bits_to_decimal(lowerCAmelCase_				)

		if output_type == "pil":
			A_		:    int						     = self.numpy_to_pil(lowerCAmelCase_				)

		if not return_dict:
			return (image,)

		return ImagePipelineOutput(images=lowerCAmelCase_				)









"""simple docstring"""
from __future__ import annotations

from decimal import Decimal
from math import *  # noqa: F403

from sympy import diff






def       __UpperCamelCase						(		snake_case__ , snake_case__ , snake_case__ = 10**-10       ):
	A_		:    Tuple						     = a
	while True:
		A_		:    List[str]						     = Decimal(snake_case__       ) - (
		    Decimal(eval(snake_case__       )       ) / Decimal(eval(str(diff(snake_case__       )       )       )       )  # noqa: S307
		)
		# This number dictates the accuracy of the answer
		if abs(eval(snake_case__       )       ) < precision:  # noqa: S307
			return float(snake_case__       )


# 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
							print(F'The root of x**2 - 5*x + 2 = 0 is {newton_raphson("x**2 - 5*x + 2", 0.4)}')
							# Find Square Root of 5
							print(F'The root of log(x) - 1 = 0 is {newton_raphson("log(x) - 1", 2)}')
							# Exponential Roots
							print(F'The root of exp(x) - 1 = 0 is {newton_raphson("exp(x) - 1", 0)}')

