


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


__UpperCamelCase					:	Optional[Any]          =				logging.get_logger(__name__)  # pylint: disable=invalid-name





@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerDiscrete
class 			lowerCAmelCase__(     snake_case__    ):






    '''simple docstring'''





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





def   snake_case_    (			__lowercase      ,							__lowercase=0.9_9_9      ,							__lowercase="cosine"      ,							):
   if alpha_transform_type == "cosine":

      def alpha_bar_fn(__lowercase							):
         return math.cos((t + 0.0_0_8) / 1.0_0_8 * math.pi / 2							) ** 2

   elif alpha_transform_type == "exp":

      def alpha_bar_fn(__lowercase							):
         return math.exp(t * -1_2.0							)

   else:
      raise ValueError(F'''Unsupported alpha_tranform_type: {alpha_transform_type}'''							)

   UpperCAmelCase_				:   str							= []
   for i in range(__lowercase							):
      UpperCAmelCase_				:   Any							= i / num_diffusion_timesteps
      UpperCAmelCase_				:   Tuple							= (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__(     snake_case__     ,     snake_case__    ):






    '''simple docstring'''





    A_	:  List[Any]								=			[e.name for e in KarrasDiffusionSchedulers]
    A_	:  Union[str, Any]								=			1





    @register_to_config
    def __init__(						self					: List[Any]							, __snake_case					: int = 1_000							, __snake_case					: float = 0.0_001							, __snake_case					: float = 0.02							, __snake_case					: str = "linear"							, __snake_case					: Optional[Union[np.ndarray, List[float]]] = None							, __snake_case					: str = "epsilon"							, __snake_case					: str = "linear"							, __snake_case					: Optional[bool] = False							, __snake_case					: str = "linspace"							, __snake_case					: int = 0							, ):





       '''simple docstring'''
       if trained_betas is not None:
          UpperCAmelCase_				:   Union[str, Any]							= torch.tensor(__snake_case							, dtype=torch.floataa						)
       elif beta_schedule == "linear":
          UpperCAmelCase_				:   List[Any]							= torch.linspace(__snake_case							, __snake_case							, __snake_case							, dtype=torch.floataa						)
       elif beta_schedule == "scaled_linear":
          # this schedule is very specific to the latent diffusion model.
          UpperCAmelCase_				:   Optional[Any]							= (
              torch.linspace(beta_start**0.5							, beta_end**0.5							, __snake_case							, dtype=torch.floataa						) ** 2
          )
       elif beta_schedule == "squaredcos_cap_v2":
          # Glide cosine schedule
          UpperCAmelCase_				:   str							= betas_for_alpha_bar(__snake_case						)
       else:
          raise NotImplementedError(f'''{beta_schedule} does is not implemented for {self.__class__}'''						)

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

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

       # setable values
       UpperCAmelCase_				:   Optional[int]							= None
       UpperCAmelCase_				:   Dict							= np.linspace(0							, num_train_timesteps - 1							, __snake_case							, dtype=__snake_case						)[::-1].copy()
       UpperCAmelCase_				:   str							= torch.from_numpy(__snake_case						)
       UpperCAmelCase_				:   Optional[Any]							= False
       UpperCAmelCase_				:   Tuple							= use_karras_sigmas





    @property
    def        _lowerCamelCase			(						self					: int						):





       '''simple docstring'''
       # 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        _lowerCamelCase			(						self					: Optional[Any]							, __snake_case					: torch.FloatTensor							, __snake_case					: Union[float, torch.FloatTensor]						):





       '''simple docstring'''
       if isinstance(__snake_case							, torch.Tensor						):
          UpperCAmelCase_				:   List[str]							= timestep.to(self.timesteps.device						)
       UpperCAmelCase_				:   str							= (self.timesteps == timestep).nonzero().item()
       UpperCAmelCase_				:   List[str]							= self.sigmas[step_index]

       UpperCAmelCase_				:   Dict							= sample / ((sigma**2 + 1) ** 0.5)

       UpperCAmelCase_				:   List[str]							= True
       return sample





    def        _lowerCamelCase			(						self					: str							, __snake_case					: int							, __snake_case					: Union[str, torch.device] = None						):





       '''simple docstring'''
       UpperCAmelCase_				:   Optional[Any]							= 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_				:   str							= np.linspace(0							, self.config.num_train_timesteps - 1							, __snake_case							, dtype=__snake_case						)[
              ::-1
          ].copy()
       elif self.config.timestep_spacing == "leading":
          UpperCAmelCase_				:   Any							= 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_				:   str							= (np.arange(0							, __snake_case						) * step_ratio).round()[::-1].copy().astype(__snake_case						)
          timesteps += self.config.steps_offset
       elif self.config.timestep_spacing == "trailing":
          UpperCAmelCase_				:   List[Any]							= 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_				:   Dict							= (np.arange(self.config.num_train_timesteps							, 0							, -step_ratio						)).round().copy().astype(__snake_case						)
          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_				:   int							= np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5						)
       UpperCAmelCase_				:   Any							= np.log(__snake_case						)

       if self.config.interpolation_type == "linear":
          UpperCAmelCase_				:   Any							= np.interp(__snake_case							, np.arange(0							, len(__snake_case						)						)							, __snake_case						)
       elif self.config.interpolation_type == "log_linear":
          UpperCAmelCase_				:   List[Any]							= torch.linspace(np.log(sigmas[-1]						)							, np.log(sigmas[0]						)							, num_inference_steps + 1						).exp()
       else:
          raise ValueError(
              f'''{self.config.interpolation_type} is not implemented. Please specify interpolation_type to either'''
              ''' \'linear\' or \'log_linear\''''						)

       if self.use_karras_sigmas:
          UpperCAmelCase_				:   Optional[int]							= self._convert_to_karras(in_sigmas=__snake_case							, num_inference_steps=self.num_inference_steps						)
          UpperCAmelCase_				:   Union[str, Any]							= np.array([self._sigma_to_t(__snake_case							, __snake_case						) for sigma in sigmas]						)

       UpperCAmelCase_				:   int							= np.concatenate([sigmas, [0.0]]						).astype(np.floataa						)
       UpperCAmelCase_				:   Dict							= torch.from_numpy(__snake_case						).to(device=__snake_case						)
       if str(__snake_case						).startswith('''mps'''						):
          # mps does not support float64
          UpperCAmelCase_				:   List[Any]							= torch.from_numpy(__snake_case						).to(__snake_case							, dtype=torch.floataa						)
       else:
          UpperCAmelCase_				:   Optional[int]							= torch.from_numpy(__snake_case						).to(device=__snake_case						)





    def        _lowerCamelCase			(						self					: List[Any]							, __snake_case					: int							, __snake_case					: List[Any]						):





       '''simple docstring'''
       # get log sigma
       UpperCAmelCase_				:   Optional[int]							= np.log(__snake_case						)

       # get distribution
       UpperCAmelCase_				:   Optional[Any]							= log_sigma - log_sigmas[:, np.newaxis]

       # get sigmas range
       UpperCAmelCase_				:   Tuple							= np.cumsum((dists >= 0)							, axis=0						).argmax(axis=0						).clip(max=log_sigmas.shape[0] - 2						)
       UpperCAmelCase_				:   Dict							= low_idx + 1

       UpperCAmelCase_				:   str							= log_sigmas[low_idx]
       UpperCAmelCase_				:   Dict							= log_sigmas[high_idx]

       # interpolate sigmas
       UpperCAmelCase_				:   Dict							= (low - log_sigma) / (low - high)
       UpperCAmelCase_				:   Dict							= np.clip(__snake_case							, 0							, 1						)

       # transform interpolation to time range
       UpperCAmelCase_				:   Union[str, Any]							= (1 - w) * low_idx + w * high_idx
       UpperCAmelCase_				:   Optional[Any]							= t.reshape(sigma.shape						)
       return t





    def        _lowerCamelCase			(						self					: Dict							, __snake_case					: torch.FloatTensor							, __snake_case					: List[Any]						):





       '''simple docstring'''
       UpperCAmelCase_				:   float							= in_sigmas[-1].item()
       UpperCAmelCase_				:   float							= in_sigmas[0].item()

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





    def        _lowerCamelCase			(						self					: str							, __snake_case					: torch.FloatTensor							, __snake_case					: Union[float, torch.FloatTensor]							, __snake_case					: torch.FloatTensor							, __snake_case					: float = 0.0							, __snake_case					: float = 0.0							, __snake_case					: float = float('''inf'''						)							, __snake_case					: float = 1.0							, __snake_case					: Optional[torch.Generator] = None							, __snake_case					: bool = True							, ):





       '''simple docstring'''

       if (
           isinstance(__snake_case							, __snake_case						)
           or isinstance(__snake_case							, torch.IntTensor						)
           or isinstance(__snake_case							, 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(__snake_case							, torch.Tensor						):
          UpperCAmelCase_				:   Any							= timestep.to(self.timesteps.device						)

       UpperCAmelCase_				:   Dict							= (self.timesteps == timestep).nonzero().item()
       UpperCAmelCase_				:   str							= self.sigmas[step_index]

       UpperCAmelCase_				:   Optional[Any]							= min(s_churn / (len(self.sigmas						) - 1)							, 2**0.5 - 1						) if s_tmin <= sigma <= s_tmax else 0.0

       UpperCAmelCase_				:   Dict							= randn_tensor(
           model_output.shape							, dtype=model_output.dtype							, device=model_output.device							, generator=__snake_case						)

       UpperCAmelCase_				:   Dict							= noise * s_noise
       UpperCAmelCase_				:   List[str]							= sigma * (gamma + 1)

       if gamma > 0:
          UpperCAmelCase_				:   Optional[Any]							= sample + eps * (sigma_hat**2 - sigma**2) ** 0.5

       # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
       # NOTE: "original_sample" should not be an expected prediction_type but is left in for
       # backwards compatibility
       if self.config.prediction_type == "original_sample" or self.config.prediction_type == "sample":
          UpperCAmelCase_				:   Optional[int]							= model_output
       elif self.config.prediction_type == "epsilon":
          UpperCAmelCase_				:   Optional[int]							= sample - sigma_hat * 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))
       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_				:   Tuple							= (sample - pred_original_sample) / sigma_hat

       UpperCAmelCase_				:   Optional[Any]							= self.sigmas[step_index + 1] - sigma_hat

       UpperCAmelCase_				:   Dict							= sample + derivative * dt

       if not return_dict:
          return (prev_sample,)

       return EulerDiscreteSchedulerOutput(prev_sample=__snake_case							, pred_original_sample=__snake_case						)





    def        _lowerCamelCase			(						self					: Optional[int]							, __snake_case					: torch.FloatTensor							, __snake_case					: torch.FloatTensor							, __snake_case					: torch.FloatTensor							, ):





       '''simple docstring'''
       # Make sure sigmas and timesteps have the same device and dtype as original_samples
       UpperCAmelCase_				:   List[str]							= self.sigmas.to(device=original_samples.device							, dtype=original_samples.dtype						)
       if original_samples.device.type == "mps" and torch.is_floating_point(__snake_case						):
          # mps does not support float64
          UpperCAmelCase_				:   Optional[int]							= self.timesteps.to(original_samples.device							, dtype=torch.floataa						)
          UpperCAmelCase_				:   Dict							= timesteps.to(original_samples.device							, dtype=torch.floataa						)
       else:
          UpperCAmelCase_				:   int							= self.timesteps.to(original_samples.device						)
          UpperCAmelCase_				:   Union[str, Any]							= timesteps.to(original_samples.device						)

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

       UpperCAmelCase_				:   Union[str, Any]							= sigmas[step_indices].flatten()
       while len(sigma.shape						) < len(original_samples.shape						):
          UpperCAmelCase_				:   Any							= sigma.unsqueeze(-1						)

       UpperCAmelCase_				:   int							= original_samples + noise * sigma
       return noisy_samples





    def __len__(						self					: Any						):





       '''simple docstring'''
       return self.config.num_train_timesteps



from __future__ import annotations

from abc import abstractmethod
from collections.abc import Iterable
from typing import Generic, Protocol, TypeVar





class 			lowerCAmelCase__(     snake_case__    ):






    '''simple docstring'''





    @abstractmethod
    def __lt__(						self					: T							, __snake_case					: T						):





       '''simple docstring'''
       pass





    @abstractmethod
    def __gt__(						self					: T							, __snake_case					: T						):





       '''simple docstring'''
       pass





    @abstractmethod
    def __eq__(						self					: T							, __snake_case					: object						):





       '''simple docstring'''
       pass





__UpperCamelCase					:	Dict          =				TypeVar('T', bound=Comparable)





class 			lowerCAmelCase__(     Generic[T]    ):






    '''simple docstring'''





    def __init__(						self					: Tuple						):





       '''simple docstring'''
       UpperCAmelCase_				:   list[T]							= []
       UpperCAmelCase_				:   int							= 0





    def __repr__(						self					: Any						):





       '''simple docstring'''
       return str(self.h						)





    def        _lowerCamelCase			(						self					: str							, __snake_case					: int						):





       '''simple docstring'''
       if child_idx > 0:
          return (child_idx - 1) // 2
       return None





    def        _lowerCamelCase			(						self					: str							, __snake_case					: int						):





       '''simple docstring'''
       UpperCAmelCase_				:   Dict							= 2 * parent_idx + 1
       if left_child_index < self.heap_size:
          return left_child_index
       return None





    def        _lowerCamelCase			(						self					: int							, __snake_case					: int						):





       '''simple docstring'''
       UpperCAmelCase_				:   Union[str, Any]							= 2 * parent_idx + 2
       if right_child_index < self.heap_size:
          return right_child_index
       return None





    def        _lowerCamelCase			(						self					: Union[str, Any]							, __snake_case					: int						):





       '''simple docstring'''
       if index < self.heap_size:
          UpperCAmelCase_				:   int							= index
          UpperCAmelCase_				:   List[str]							= self.left_child_idx(__snake_case						)
          UpperCAmelCase_				:   List[str]							= self.right_child_idx(__snake_case						)
          # check which child is larger than its parent
          if left_child is not None and self.h[left_child] > self.h[violation]:
             UpperCAmelCase_				:   List[str]							= left_child
          if right_child is not None and self.h[right_child] > self.h[violation]:
             UpperCAmelCase_				:   List[str]							= right_child
          # if violation indeed exists
          if violation != index:
             # swap to fix the violation
             UpperCAmelCase_		,   UpperCAmelCase_				:   List[Any]							= self.h[index], self.h[violation]
             # fix the subsequent violation recursively if any
             self.max_heapify(__snake_case						)





    def        _lowerCamelCase			(						self					: Optional[Any]							, __snake_case					: Iterable[T]						):





       '''simple docstring'''
       UpperCAmelCase_				:   Union[str, Any]							= list(__snake_case						)
       UpperCAmelCase_				:   int							= len(self.h						)
       if self.heap_size > 1:
          # max_heapify from right to left but exclude leaves (last level)
          for i in range(self.heap_size // 2 - 1							, -1							, -1						):
             self.max_heapify(__snake_case						)





    def        _lowerCamelCase			(						self					: Tuple						):





       '''simple docstring'''
       if self.heap_size >= 2:
          UpperCAmelCase_				:   List[str]							= self.h[0]
          UpperCAmelCase_				:   Dict							= self.h.pop(-1						)
          self.heap_size -= 1
          self.max_heapify(0						)
          return me
       elif self.heap_size == 1:
          self.heap_size -= 1
          return self.h.pop(-1						)
       else:
          raise Exception('''Empty heap'''						)





    def        _lowerCamelCase			(						self					: List[str]							, __snake_case					: T						):





       '''simple docstring'''
       self.h.append(__snake_case						)
       UpperCAmelCase_				:   Tuple							= (self.heap_size - 1) // 2
       self.heap_size += 1
       while idx >= 0:
          self.max_heapify(__snake_case						)
          UpperCAmelCase_				:   int							= (idx - 1) // 2





    def        _lowerCamelCase			(						self					: List[str]						):





       '''simple docstring'''
       UpperCAmelCase_				:   Tuple							= self.heap_size
       for j in range(size - 1							, 0							, -1						):
          UpperCAmelCase_		,   UpperCAmelCase_				:   Any							= self.h[j], self.h[0]
          self.heap_size -= 1
          self.max_heapify(0						)
       UpperCAmelCase_				:   Union[str, Any]							= size


if __name__ == "__main__":
       import doctest

       # run doc test
       doctest.testmod()

       # demo
       for unsorted in [
           [0],
           [2],
           [3, 5],
           [5, 3],
           [5, 5],
           [0, 0, 0, 0],
           [1, 1, 1, 1],
           [2, 2, 3, 5],
           [0, 2, 2, 3, 5],
           [2, 5, 3, 0, 2, 3, 0, 3],
           [6, 1, 2, 7, 9, 3, 4, 5, 10, 8],
           [103, 9, 1, 7, 11, 15, 25, 201, 209, 107, 5],
           [-45, -2, -5],
       ]:
              print(F'unsorted array: {unsorted}')

              __UpperCamelCase					:	Heap[int]          =				Heap()
              heap.build_max_heap(unsorted)
              print(F'after build heap: {heap}')

              print(F'max value: {heap.extract_max()}')
              print(F'after max value removed: {heap}')

              heap.insert(100)
              print(F'after new value 100 inserted: {heap}')

              heap.heap_sort()
              print(F'heap-sorted array: {heap}\n')