






import math
import warnings
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch
from scipy import integrate

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin

@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->LMSDiscrete
class        _SCREAMING_SNAKE_CASE			(     _a ):
	snake_case__				:	torch.FloatTensor
	snake_case__				:	Optional[torch.FloatTensor]	      =    None

def   SCREAMING_SNAKE_CASE_				(				__magic_name__   :    List[Any]      ,     __magic_name__   :    Union[str, Any]=0.999      ,     __magic_name__   :    Optional[Any]="cosine"      ,     )						->     Union[str, Any]:






	"""simple docstring"""



	if alpha_transform_type == "cosine":

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

	elif alpha_transform_type == "exp":

		def alpha_bar_fn(__magic_name__   :    Optional[Any]   ):
			return math.exp(t * -12.0   )

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

	UpperCamelCase	:str		=      []
	for i in range(__magic_name__   ):
		UpperCamelCase	:Optional[Any]		=      i / num_diffusion_timesteps
		UpperCamelCase	:Dict		=      (i + 1) / num_diffusion_timesteps
		betas.append(min(1 - alpha_bar_fn(__magic_name__   ) / alpha_bar_fn(__magic_name__   )      ,     __magic_name__   )   )
	return torch.tensor(__magic_name__      ,     dtype=torch.floataa   )

class        _SCREAMING_SNAKE_CASE			(     _a						,  _a ):
	snake_case__				:	Tuple	      =    [e.name for e in KarrasDiffusionSchedulers]
	snake_case__				:	Union[str, Any]	      =    1





	@register_to_config
	def __init__(						self							:   List[str]					,    __lowerCamelCase							:   int = 1_000					,    __lowerCamelCase							:   float = 0.0001					,    __lowerCamelCase							:   float = 0.02					,    __lowerCamelCase							:   str = "linear"					,    __lowerCamelCase							:   Optional[Union[np.ndarray, List[float]]] = None					,    __lowerCamelCase							:   Optional[bool] = False					,    __lowerCamelCase							:   str = "epsilon"					,    __lowerCamelCase							:   str = "linspace"					,    __lowerCamelCase							:   int = 0					,    ):
		if trained_betas is not None:
			UpperCamelCase	:Optional[int]		=      torch.tensor(__lowerCamelCase					,    dtype=torch.floataa      )
		elif beta_schedule == "linear":
			UpperCamelCase	:Union[str, Any]		=      torch.linspace(__lowerCamelCase					,    __lowerCamelCase					,    __lowerCamelCase					,    dtype=torch.floataa      )
		elif beta_schedule == "scaled_linear":
			# this schedule is very specific to the latent diffusion model.
			UpperCamelCase	:Tuple		=      (
			    torch.linspace(beta_start**0.5					,    beta_end**0.5					,    __lowerCamelCase					,    dtype=torch.floataa      ) ** 2
			)
		elif beta_schedule == "squaredcos_cap_v2":
			# Glide cosine schedule
			UpperCamelCase	:List[Any]		=      betas_for_alpha_bar(__lowerCamelCase      )
		else:
			raise NotImplementedError(F"""{beta_schedule} does is not implemented for {self.__class__}"""      )

		UpperCamelCase	:List[str]		=      1.0 - self.betas
		UpperCamelCase	:List[Any]		=      torch.cumprod(self.alphas					,    dim=0      )

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

		# setable values
		UpperCamelCase	:Optional[Any]		=      None
		UpperCamelCase	:Optional[int]		=      use_karras_sigmas
		self.set_timesteps(__lowerCamelCase					,    __lowerCamelCase      )
		UpperCamelCase	:Union[str, Any]		=      []
		UpperCamelCase	:Optional[Any]		=      False





	@property
	def 		_A					(						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 		_A					(						self							:   Any					,    __lowerCamelCase							:   torch.FloatTensor					,    __lowerCamelCase							:   Union[float, torch.FloatTensor]      ):
		if isinstance(__lowerCamelCase					,    torch.Tensor      ):
			UpperCamelCase	:Tuple		=      timestep.to(self.timesteps.device      )
		UpperCamelCase	:List[Any]		=      (self.timesteps == timestep).nonzero().item()
		UpperCamelCase	:int		=      self.sigmas[step_index]
		UpperCamelCase	:Union[str, Any]		=      sample / ((sigma**2 + 1) ** 0.5)
		UpperCamelCase	:Optional[int]		=      True
		return sample





	def 		_A					(						self							:   Any					,    __lowerCamelCase							:   Optional[int]					,    __lowerCamelCase							:   Tuple					,    __lowerCamelCase							:   int      ):

		def lms_derivative(__lowerCamelCase							:   Dict      ):
			UpperCamelCase	:Optional[Any]		=      1.0
			for k in range(__lowerCamelCase      ):
				if current_order == k:
					continue
				prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
			return prod

		UpperCamelCase	:Any		=      integrate.quad(__lowerCamelCase					,    self.sigmas[t]					,    self.sigmas[t + 1]					,    epsrel=1E-4      )[0]

		return integrated_coeff





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

		UpperCamelCase	:Tuple		=      np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5      )
		UpperCamelCase	:List[Any]		=      np.log(__lowerCamelCase      )
		UpperCamelCase	:Optional[Any]		=      np.interp(__lowerCamelCase					,    np.arange(0					,    len(__lowerCamelCase      )      )					,    __lowerCamelCase      )

		if self.use_karras_sigmas:
			UpperCamelCase	:int		=      self._convert_to_karras(in_sigmas=__lowerCamelCase      )
			UpperCamelCase	:List[str]		=      np.array([self._sigma_to_t(__lowerCamelCase					,    __lowerCamelCase      ) for sigma in sigmas]      )

		UpperCamelCase	:Optional[int]		=      np.concatenate([sigmas, [0.0]]      ).astype(np.floataa      )

		UpperCamelCase	:Optional[Any]		=      torch.from_numpy(__lowerCamelCase      ).to(device=__lowerCamelCase      )
		if str(__lowerCamelCase      ).startswith("""mps"""      ):
			# mps does not support float64
			UpperCamelCase	:Dict		=      torch.from_numpy(__lowerCamelCase      ).to(__lowerCamelCase					,    dtype=torch.floataa      )
		else:
			UpperCamelCase	:Union[str, Any]		=      torch.from_numpy(__lowerCamelCase      ).to(device=__lowerCamelCase      )

		UpperCamelCase	:Union[str, Any]		=      []





	def 		_A					(						self							:   Any					,    __lowerCamelCase							:   str					,    __lowerCamelCase							:   Union[str, Any]      ):
		# get log sigma
		UpperCamelCase	:Optional[Any]		=      np.log(__lowerCamelCase      )

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

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

		UpperCamelCase	:Dict		=      log_sigmas[low_idx]
		UpperCamelCase	:Union[str, Any]		=      log_sigmas[high_idx]

		# interpolate sigmas
		UpperCamelCase	:Dict		=      (low - log_sigma) / (low - high)
		UpperCamelCase	:Optional[Any]		=      np.clip(__lowerCamelCase					,    0					,    1      )

		# transform interpolation to time range
		UpperCamelCase	:str		=      (1 - w) * low_idx + w * high_idx
		UpperCamelCase	:Tuple		=      t.reshape(sigma.shape      )
		return t





	def 		_A					(						self							:   Dict					,    __lowerCamelCase							:   torch.FloatTensor      ):
		UpperCamelCase	:float		=      in_sigmas[-1].item()
		UpperCamelCase	:float		=      in_sigmas[0].item()

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





	def 		_A					(						self							:   int					,    __lowerCamelCase							:   torch.FloatTensor					,    __lowerCamelCase							:   Union[float, torch.FloatTensor]					,    __lowerCamelCase							:   torch.FloatTensor					,    __lowerCamelCase							:   int = 4					,    __lowerCamelCase							:   bool = True					,    ):
		if not self.is_scale_input_called:
			warnings.warn(
			    """The `scale_model_input` function should be called before `step` to ensure correct denoising. """
			    """See `StableDiffusionPipeline` for a usage example."""      )

		if isinstance(__lowerCamelCase					,    torch.Tensor      ):
			UpperCamelCase	:Optional[int]		=      timestep.to(self.timesteps.device      )
		UpperCamelCase	:List[Any]		=      (self.timesteps == timestep).nonzero().item()
		UpperCamelCase	:Union[str, Any]		=      self.sigmas[step_index]

		# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
		if self.config.prediction_type == "epsilon":
			UpperCamelCase	:List[str]		=      sample - sigma * model_output
		elif self.config.prediction_type == "v_prediction":
			# * c_out + input * c_skip
			UpperCamelCase	:Any		=      model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
		elif self.config.prediction_type == "sample":
			UpperCamelCase	:List[Any]		=      model_output
		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
		UpperCamelCase	:Dict		=      (sample - pred_original_sample) / sigma
		self.derivatives.append(__lowerCamelCase      )
		if len(self.derivatives      ) > order:
			self.derivatives.pop(0      )

		# 3. Compute linear multistep coefficients
		UpperCamelCase	:int		=      min(step_index + 1					,    __lowerCamelCase      )
		UpperCamelCase	:Tuple		=      [self.get_lms_coefficient(__lowerCamelCase					,    __lowerCamelCase					,    __lowerCamelCase      ) for curr_order in range(__lowerCamelCase      )]

		# 4. Compute previous sample based on the derivatives path
		UpperCamelCase	:Any		=      sample + sum(
		    coeff * derivative for coeff, derivative in zip(__lowerCamelCase					,    reversed(self.derivatives      )      )      )

		if not return_dict:
			return (prev_sample,)

		return LMSDiscreteSchedulerOutput(prev_sample=__lowerCamelCase					,    pred_original_sample=__lowerCamelCase      )





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

		UpperCamelCase	:Dict		=      [(schedule_timesteps == t).nonzero().item() for t in timesteps]

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

		UpperCamelCase	:Optional[int]		=      original_samples + noise * sigma
		return noisy_samples





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








class        _SCREAMING_SNAKE_CASE			:





	def __init__(						self							:   Tuple      ):
		UpperCamelCase	:List[str]		=      [0]
		UpperCamelCase	:Optional[int]		=      0





	def 		_A					(						self							:   Dict					,    __lowerCamelCase							:   int      ):
		UpperCamelCase	:List[str]		=      self.__heap[i]
		while i // 2 > 0:
			if self.__heap[i] > self.__heap[i // 2]:
				UpperCamelCase	:Any		=      self.__heap[i // 2]
				UpperCamelCase	:Optional[Any]		=      temporary
			i //= 2





	def 		_A					(						self							:   Optional[int]					,    __lowerCamelCase							:   int      ):
		self.__heap.append(__lowerCamelCase      )
		self.__size += 1
		self.__swap_up(self.__size      )





	def 		_A					(						self							:   Optional[Any]					,    __lowerCamelCase							:   int      ):
		while self.__size >= 2 * i:
			if 2 * i + 1 > self.__size:
				UpperCamelCase	:List[Any]		=      2 * i
			else:
				if self.__heap[2 * i] > self.__heap[2 * i + 1]:
					UpperCamelCase	:Union[str, Any]		=      2 * i
				else:
					UpperCamelCase	:Dict		=      2 * i + 1
			UpperCamelCase	:Optional[Any]		=      self.__heap[i]
			if self.__heap[i] < self.__heap[bigger_child]:
				UpperCamelCase	:List[str]		=      self.__heap[bigger_child]
				UpperCamelCase	:List[str]		=      temporary
			UpperCamelCase	:Optional[int]		=      bigger_child





	def 		_A					(						self							:   Optional[Any]      ):
		UpperCamelCase	:str		=      self.__heap[1]
		UpperCamelCase	:Tuple		=      self.__heap[self.__size]
		self.__size -= 1
		self.__heap.pop()
		self.__swap_down(1      )
		return max_value





	@property
	def 		_A					(						self							:   int      ):
		return self.__heap[1:]





	def __len__(						self							:   str      ):
		return self.__size


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	# create an instance of BinaryHeap
	UpperCAmelCase_					:		Optional[int]           = BinaryHeap()
	binary_heap.insert(6)
	binary_heap.insert(10)
	binary_heap.insert(15)
	binary_heap.insert(12)
	# pop root(max-values because it is max heap)
	print(binary_heap.pop())  # 15
	print(binary_heap.pop())  # 12
	# get the list and size after operations
	print(binary_heap.get_list)
	print(len(binary_heap))
