'''simple docstring'''


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			):







  '''simple docstring'''






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







def    _lowerCamelCase       ( lowerCamelCase_   :				List[Any]      ,	lowerCamelCase_   :				Union[str, Any]=0.999      ,	lowerCamelCase_   :				Optional[Any]="cosine"      ,	):



     """simple docstring"""





     if alpha_transform_type == "cosine":

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

     elif alpha_transform_type == "exp":

          def alpha_bar_fn(lowerCamelCase_   :				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(lowerCamelCase_  ):
          UpperCAmelCase_				:  Optional[Any]  = i / num_diffusion_timesteps
          UpperCAmelCase_				:  Dict  = (i + 1) / num_diffusion_timesteps
          betas.append(min(1 - alpha_bar_fn(lowerCamelCase_  ) / alpha_bar_fn(lowerCamelCase_  )      ,	lowerCamelCase_  )  )
     return torch.tensor(lowerCamelCase_      ,	dtype=torch.floataa  )






class 	__SCREAMING_SNAKE_CASE		(			_a		,      _a			):







  '''simple docstring'''






  lowerCamelCase_						:Tuple		       =						[e.name for e in KarrasDiffusionSchedulers]
  lowerCamelCase_						:Union[str, Any]		       =						1


  @register_to_config
  def __init__(					self ,						snake_case_ = 1_0_0_0 ,						snake_case_ = 0.00_01 ,						snake_case_ = 0.02 ,						snake_case_ = "linear" ,						snake_case_ = None ,						snake_case_ = False ,						snake_case_ = "epsilon" ,						snake_case_ = "linspace" ,						snake_case_ = 0 ,						):




       '''simple docstring'''

       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 _UpperCamelCase	(					self		):




       '''simple docstring'''

       if self.config.timestep_spacing in ["linspace", "trailing"]:
            return self.sigmas.max()

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


  def _UpperCamelCase	(					self ,						snake_case_ ,						snake_case_		):




       '''simple docstring'''

       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 _UpperCamelCase	(					self ,						snake_case_ ,						snake_case_ ,						snake_case_		):




       '''simple docstring'''

       def lms_derivative(snake_case_		):
            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 _UpperCamelCase	(					self ,						snake_case_ ,						snake_case_ = None		):




       '''simple docstring'''

       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 _UpperCamelCase	(					self ,						snake_case_ ,						snake_case_		):




       '''simple docstring'''

       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 _UpperCamelCase	(					self ,						snake_case_		):




       '''simple docstring'''

       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 _UpperCamelCase	(					self ,						snake_case_ ,						snake_case_ ,						snake_case_ ,						snake_case_ = 4 ,						snake_case_ = True ,						):




       '''simple docstring'''

       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 _UpperCamelCase	(					self ,						snake_case_ ,						snake_case_ ,						snake_case_ ,						):




       '''simple docstring'''

       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		):




       '''simple docstring'''

       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))
