



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


snake_case     :    str						=    logging.get_logger(__name__)  # pylint: disable=invalid-name




@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerAncestralDiscrete
class 				lowerCAmelCase__	(						__lowerCAmelCase    ):
					__A  :     Tuple     =    42
					__A  :     Optional[Any]     =    None




def 						snake_case__							(       __lowercase				,  __lowercase=0.999				,  __lowercase="cosine"				,  )		->		Optional[int]:







						"""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}'							)

						A__						:				str         =			[]
						for i in range(__lowercase							):
												A__						:				Union[str, Any]         =			i / num_diffusion_timesteps
												A__						:				Any         =			(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 				lowerCAmelCase__	(						__lowerCAmelCase       ,				__lowerCAmelCase    ):
					__A  :     Tuple     =    [e.name for e in KarrasDiffusionSchedulers]
					__A  :     Optional[int]     =    1







					@register_to_config
					def __init__(							self   :  Any      ,		_A   :  Union[str, Any] = 1000      ,		_A   :  Any = 0.00_01      ,		_A   :  str = 0.02      ,		_A   :  List[Any] = "linear"      ,		_A   :  str = None      ,		_A   :  Union[str, Any] = "epsilon"      ,		_A   :  Tuple = "linspace"      ,		_A   :  str = 0      ,		):
											if trained_betas is not None:
																	A__						:				List[str]         =			torch.tensor(lowercase_      ,		dtype=torch.floataa)
											elif beta_schedule == "linear":
																	A__						:				Dict         =			torch.linspace(lowercase_      ,		lowercase_      ,		lowercase_      ,		dtype=torch.floataa)
											elif beta_schedule == "scaled_linear":
																	# this schedule is very specific to the latent diffusion model.
																	A__						:				Tuple         =			(
																	    torch.linspace(beta_start**0.5      ,		beta_end**0.5      ,		lowercase_      ,		dtype=torch.floataa) ** 2
																	)
											elif beta_schedule == "squaredcos_cap_v2":
																	# Glide cosine schedule
																	A__						:				List[Any]         =			betas_for_alpha_bar(lowercase_)
											else:
																	raise NotImplementedError(F'{beta_schedule} does is not implemented for {self.__class__}')

											A__						:				Union[str, Any]         =			1.0 - self.betas
											A__						:				Tuple         =			torch.cumprod(self.alphas      ,		dim=0)

											A__						:				Optional[int]         =			np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
											A__						:				str         =			np.concatenate([sigmas[::-1], [0.0]]).astype(np.floataa)
											A__						:				List[Any]         =			torch.from_numpy(lowercase_)

											# setable values
											A__						:				str         =			None
											A__						:				Dict         =			np.linspace(0      ,		num_train_timesteps - 1      ,		lowercase_      ,		dtype=lowercase_)[::-1].copy()
											A__						:				Any         =			torch.from_numpy(lowercase_)
											A__						:				List[str]         =			False







					@property
					def 			_lowercase      (							self   :  List[str]):
											# standard deviation of the initial noise distribution
											if self.config.timestep_spacing in ["linspace", "trailing"]:
																	return self.sigmas.max()

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







					def 			_lowercase      (							self   :  str      ,		_A   :  Any      ,		_A   :  Tuple):
											if isinstance(lowercase_      ,		torch.Tensor):
																	A__						:				Tuple         =			timestep.to(self.timesteps.device)
											A__						:				Any         =			(self.timesteps == timestep).nonzero().item()
											A__						:				List[Any]         =			self.sigmas[step_index]
											A__						:				str         =			sample / ((sigma**2 + 1) ** 0.5)
											A__						:				str         =			True
											return sample







					def 			_lowercase      (							self   :  List[str]      ,		_A   :  str      ,		_A   :  Optional[int] = None):
											A__						:				List[str]         =			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":
																	A__						:				Optional[Any]         =			np.linspace(0      ,		self.config.num_train_timesteps - 1      ,		lowercase_      ,		dtype=lowercase_)[
																	    ::-1
																	].copy()
											elif self.config.timestep_spacing == "leading":
																	A__						:				List[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
																	A__						:				Optional[Any]         =			(np.arange(0      ,		lowercase_) * step_ratio).round()[::-1].copy().astype(lowercase_)
																	timesteps += self.config.steps_offset
											elif self.config.timestep_spacing == "trailing":
																	A__						:				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
																	A__						:				Any         =			(np.arange(self.config.num_train_timesteps      ,		0      ,		-step_ratio)).round().copy().astype(lowercase_)
																	timesteps -= 1
											else:
																	raise ValueError(
																	    F'{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.')

											A__						:				Optional[int]         =			np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
											A__						:				Any         =			np.interp(lowercase_      ,		np.arange(0      ,		len(lowercase_))      ,		lowercase_)
											A__						:				List[Any]         =			np.concatenate([sigmas, [0.0]]).astype(np.floataa)
											A__						:				Tuple         =			torch.from_numpy(lowercase_).to(device=lowercase_)
											if str(lowercase_).startswith("mps"):
																	# mps does not support float64
																	A__						:				Optional[int]         =			torch.from_numpy(lowercase_).to(lowercase_      ,		dtype=torch.floataa)
											else:
																	A__						:				Tuple         =			torch.from_numpy(lowercase_).to(device=lowercase_)







					def 			_lowercase      (							self   :  int      ,		_A   :  Dict      ,		_A   :  Any      ,		_A   :  str      ,		_A   :  str = None      ,		_A   :  Tuple = True      ,		):

											if (
											    isinstance(lowercase_      ,		lowercase_)
											    or isinstance(lowercase_      ,		torch.IntTensor)
											    or isinstance(lowercase_      ,		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(lowercase_      ,		torch.Tensor):
																	A__						:				str         =			timestep.to(self.timesteps.device)

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

											# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
											if self.config.prediction_type == "epsilon":
																	A__						:				Optional[Any]         =			sample - sigma * model_output
											elif self.config.prediction_type == "v_prediction":
																	# * c_out + input * c_skip
																	A__						:				Optional[int]         =			model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
											elif self.config.prediction_type == "sample":
																	raise NotImplementedError("prediction_type not implemented yet: sample")
											else:
																	raise ValueError(
																	    F'prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`')

											A__						:				Union[str, Any]         =			self.sigmas[step_index]
											A__						:				List[str]         =			self.sigmas[step_index + 1]
											A__						:				Union[str, Any]         =			(sigma_to**2 * (sigma_from**2 - sigma_to**2) / sigma_from**2) ** 0.5
											A__						:				int         =			(sigma_to**2 - sigma_up**2) ** 0.5

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

											A__						:				int         =			sigma_down - sigma

											A__						:				Any         =			sample + derivative * dt

											A__						:				Any         =			model_output.device
											A__						:				int         =			randn_tensor(model_output.shape      ,		dtype=model_output.dtype      ,		device=lowercase_      ,		generator=lowercase_)

											A__						:				Dict         =			prev_sample + noise * sigma_up

											if not return_dict:
																	return (prev_sample,)

											return EulerAncestralDiscreteSchedulerOutput(
											    prev_sample=lowercase_      ,		pred_original_sample=lowercase_)







					def 			_lowercase      (							self   :  List[str]      ,		_A   :  Dict      ,		_A   :  Dict      ,		_A   :  Any      ,		):
											# Make sure sigmas and timesteps have the same device and dtype as original_samples
											A__						:				int         =			self.sigmas.to(device=original_samples.device      ,		dtype=original_samples.dtype)
											if original_samples.device.type == "mps" and torch.is_floating_point(lowercase_):
																	# mps does not support float64
																	A__						:				Optional[int]         =			self.timesteps.to(original_samples.device      ,		dtype=torch.floataa)
																	A__						:				int         =			timesteps.to(original_samples.device      ,		dtype=torch.floataa)
											else:
																	A__						:				Any         =			self.timesteps.to(original_samples.device)
																	A__						:				Any         =			timesteps.to(original_samples.device)

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

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

											A__						:				str         =			original_samples + noise * sigma
											return noisy_samples







					def __len__(							self   :  Optional[int]):
											return self.config.num_train_timesteps


'''simple docstring'''

from .balanced_parentheses import balanced_parentheses
from .stack import Stack

def      __magic_name__							(			A				)      ->		int:
	return {"+": 1, "-": 1, "*": 2, "/": 2, "^": 3}.get(A       , -1				)

def      __magic_name__							(			A				)      ->		str:
	if not balanced_parentheses(A				):
		raise ValueError('Mismatched parentheses'				)
	snake_case							=					Stack()
	snake_case							=					[]
	for char in expression_str:
		if char.isalpha() or char.isdigit():
			postfix.append(A				)
		elif char == "(":
			stack.push(A				)
		elif char == ")":
			while not stack.is_empty() and stack.peek() != "(":
				postfix.append(stack.pop()				)
			stack.pop()
		else:
			while not stack.is_empty() and precedence(A				) <= precedence(stack.peek()				):
				postfix.append(stack.pop()				)
			stack.push(A				)
	while not stack.is_empty():
		postfix.append(stack.pop()				)
	return " ".join(A				)


if __name__ == "__main__":
						from doctest import testmod

						testmod()
						lowerCAmelCase_     =      "a+b*(c^d-e)^(f+g*h)-i"

						print("Infix to Postfix Notation demonstration:\n")
						print("Infix notation: " + expression)
						print("Postfix notation: " + infix_to_postfix(expression))





