

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







@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerAncestralDiscrete
class     a__    (				UpperCAmelCase    ):







		"""simple docstring"""




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






def    __lowercase (       _A  ,      _A=0.999  ,      _A="cosine"  ,      )       ->  Dict:




						if alpha_transform_type == "cosine":

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

						elif alpha_transform_type == "exp":

												def alpha_bar_fn(_A     ):
																		return math.exp(t * -12.0     )

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

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







class     a__    (				UpperCAmelCase		,     UpperCAmelCase    ):







		"""simple docstring"""




		UpperCAmelCase__ :	str         =[e.name for e in KarrasDiffusionSchedulers]
		UpperCAmelCase__ :	Tuple         =1


		@register_to_config
		def __init__(     self      :	List[Any]			,			UpperCAmelCase__      :	int = 1_0_0_0			,			UpperCAmelCase__      :	float = 0.00_01			,			UpperCAmelCase__      :	float = 0.02			,			UpperCAmelCase__      :	str = "linear"			,			UpperCAmelCase__      :	Optional[Union[np.ndarray, List[float]]] = None			,			UpperCAmelCase__      :	str = "epsilon"			,			UpperCAmelCase__      :	str = "linspace"			,			UpperCAmelCase__      :	int = 0			,			)   ->Optional[Any]:
								"""simple docstring"""







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

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

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

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


		@property
		def 	_lowercase (     self      :	str						)   ->Tuple:
								"""simple docstring"""







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

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


		def 	_lowercase (     self      :	Tuple			,			UpperCAmelCase__      :	torch.FloatTensor			,			UpperCAmelCase__      :	Union[float, torch.FloatTensor]						)   ->int:
								"""simple docstring"""







								if isinstance(UpperCAmelCase__			,			torch.Tensor						):
														SCREAMING_SNAKE_CASE	: Any					       =				timestep.to(self.timesteps.device						)
								SCREAMING_SNAKE_CASE	: Any					       =				(self.timesteps == timestep).nonzero().item()
								SCREAMING_SNAKE_CASE	: Dict					       =				self.sigmas[step_index]
								SCREAMING_SNAKE_CASE	: str					       =				sample / ((sigma**2 + 1) ** 0.5)
								SCREAMING_SNAKE_CASE	: Union[str, Any]					       =				True
								return sample


		def 	_lowercase (     self      :	Dict			,			UpperCAmelCase__      :	int			,			UpperCAmelCase__      :	Union[str, torch.device] = None						)   ->int:
								"""simple docstring"""







								SCREAMING_SNAKE_CASE	: 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":
														SCREAMING_SNAKE_CASE	: Union[str, Any]					       =				np.linspace(0			,			self.config.num_train_timesteps - 1			,			UpperCAmelCase__			,			dtype=UpperCAmelCase__						)[
														    ::-1
														].copy()
								elif self.config.timestep_spacing == "leading":
														SCREAMING_SNAKE_CASE	: Union[str, 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
														SCREAMING_SNAKE_CASE	: Tuple					       =				(np.arange(0			,			UpperCAmelCase__						) * step_ratio).round()[::-1].copy().astype(UpperCAmelCase__						)
														timesteps += self.config.steps_offset
								elif self.config.timestep_spacing == "trailing":
														SCREAMING_SNAKE_CASE	: 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
														SCREAMING_SNAKE_CASE	: Optional[Any]					       =				(np.arange(self.config.num_train_timesteps			,			0			,			-step_ratio						)).round().copy().astype(UpperCAmelCase__						)
														timesteps -= 1
								else:
														raise ValueError(
														    f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'."						)

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


		def 	_lowercase (     self      :	str			,			UpperCAmelCase__      :	torch.FloatTensor			,			UpperCAmelCase__      :	Union[float, torch.FloatTensor]			,			UpperCAmelCase__      :	torch.FloatTensor			,			UpperCAmelCase__      :	Optional[torch.Generator] = None			,			UpperCAmelCase__      :	bool = True			,			)   ->List[Any]:
								"""simple docstring"""







								if (
								    isinstance(UpperCAmelCase__			,			UpperCAmelCase__						)
								    or isinstance(UpperCAmelCase__			,			torch.IntTensor						)
								    or isinstance(UpperCAmelCase__			,			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(UpperCAmelCase__			,			torch.Tensor						):
														SCREAMING_SNAKE_CASE	: Tuple					       =				timestep.to(self.timesteps.device						)

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

								# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
								if self.config.prediction_type == "epsilon":
														SCREAMING_SNAKE_CASE	: List[str]					       =				sample - sigma * model_output
								elif self.config.prediction_type == "v_prediction":
														# * c_out + input * c_skip
														SCREAMING_SNAKE_CASE	: Any					       =				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`"						)

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

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

								SCREAMING_SNAKE_CASE	: Optional[int]					       =				sigma_down - sigma

								SCREAMING_SNAKE_CASE	: Dict					       =				sample + derivative * dt

								SCREAMING_SNAKE_CASE	: Optional[int]					       =				model_output.device
								SCREAMING_SNAKE_CASE	: Dict					       =				randn_tensor(model_output.shape			,			dtype=model_output.dtype			,			device=UpperCAmelCase__			,			generator=UpperCAmelCase__						)

								SCREAMING_SNAKE_CASE	: List[str]					       =				prev_sample + noise * sigma_up

								if not return_dict:
														return (prev_sample,)

								return EulerAncestralDiscreteSchedulerOutput(
								    prev_sample=UpperCAmelCase__			,			pred_original_sample=UpperCAmelCase__						)


		def 	_lowercase (     self      :	str			,			UpperCAmelCase__      :	torch.FloatTensor			,			UpperCAmelCase__      :	torch.FloatTensor			,			UpperCAmelCase__      :	torch.FloatTensor			,			)   ->int:
								"""simple docstring"""







								SCREAMING_SNAKE_CASE	: Union[str, Any]					       =				self.sigmas.to(device=original_samples.device			,			dtype=original_samples.dtype						)
								if original_samples.device.type == "mps" and torch.is_floating_point(UpperCAmelCase__						):
														# mps does not support float64
														SCREAMING_SNAKE_CASE	: Tuple					       =				self.timesteps.to(original_samples.device			,			dtype=torch.floataa						)
														SCREAMING_SNAKE_CASE	: List[Any]					       =				timesteps.to(original_samples.device			,			dtype=torch.floataa						)
								else:
														SCREAMING_SNAKE_CASE	: List[str]					       =				self.timesteps.to(original_samples.device						)
														SCREAMING_SNAKE_CASE	: Tuple					       =				timesteps.to(original_samples.device						)

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

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

								SCREAMING_SNAKE_CASE	: List[str]					       =				original_samples + noise * sigma
								return noisy_samples




		def __len__(     self      :	Optional[int]						)   ->Dict:
								"""simple docstring"""







								return self.config.num_train_timesteps







from __future__ import annotations

UpperCAmelCase__	:       Optional[int]			      =      [2, 1, 4, 5, 6, 0, 8, 9, 1, 2, 0, 6, 4, 2, 0, 6, 5, 3, 2, 7]







class     a__    :







  """simple docstring"""




  def __init__(     self      :	Optional[Any]			,			UpperCAmelCase__      :	int						)   ->None:
        """simple docstring"""







        SCREAMING_SNAKE_CASE	: int					       =				-1
        SCREAMING_SNAKE_CASE	: int					       =				-1
        SCREAMING_SNAKE_CASE	: list[int]					       =				[-1] * length
        SCREAMING_SNAKE_CASE	: Node | None					       =				None
        SCREAMING_SNAKE_CASE	: Node | None					       =				None




  def __repr__(     self      :	Dict						)   ->str:
        """simple docstring"""







        return f"Node(min_value={self.minn} max_value={self.maxx})"






def    __lowercase (       _A     )       ->  Node | None:
      SCREAMING_SNAKE_CASE	: Tuple					       =				Node(len(_A     )     )
      SCREAMING_SNAKE_CASE       ,		SCREAMING_SNAKE_CASE	: int					       =				min(_A     ), max(_A     )
      # Leaf node case where the node contains only one unique value
      if root.minn == root.maxx:
            return root
      SCREAMING_SNAKE_CASE	: int					       =				(root.minn + root.maxx) // 2

      SCREAMING_SNAKE_CASE	: list[int]					       =				[]
      SCREAMING_SNAKE_CASE	: list[int]					       =				[]

      for index, num in enumerate(_A     ):
            if num <= pivot:
                  left_arr.append(_A     )
            else:
                  right_arr.append(_A     )
            SCREAMING_SNAKE_CASE	: int					       =				len(_A     )
      SCREAMING_SNAKE_CASE	: int					       =				build_tree(_A     )
      SCREAMING_SNAKE_CASE	: Tuple					       =				build_tree(_A     )
      return root






def    __lowercase (       _A  ,      _A  ,      _A     )       ->  int:
      if index < 0 or node is None:
            return 0
      # Leaf node cases
      if node.minn == node.maxx:
            return index + 1 if node.minn == num else 0
      SCREAMING_SNAKE_CASE	: List[str]					       =				(node.minn + node.maxx) // 2
      if num <= pivot:
            # go the left subtree and map index to the left subtree
            return rank_till_index(node.left  ,      _A  ,      node.map_left[index] - 1     )
      else:
            # go to the right subtree and map index to the right subtree
            return rank_till_index(node.right  ,      _A  ,      index - node.map_left[index]     )






def    __lowercase (       _A  ,      _A  ,      _A  ,      _A     )       ->  int:
      if start > end:
            return 0
      SCREAMING_SNAKE_CASE	: Any					       =				rank_till_index(_A  ,      _A  ,      _A     )
      SCREAMING_SNAKE_CASE	: Optional[int]					       =				rank_till_index(_A  ,      _A  ,      start - 1     )
      return rank_till_end - rank_before_start






def    __lowercase (       _A  ,      _A  ,      _A  ,      _A     )       ->  int:
      if index > (end - start) or start > end or node is None:
            return -1
      # Leaf node case
      if node.minn == node.maxx:
            return node.minn
      # Number of elements in the left subtree in interval [start, end]
      SCREAMING_SNAKE_CASE	: Tuple					       =				node.map_left[end] - (
          node.map_left[start - 1] if start else 0
      )
      if num_elements_in_left_tree > index:
            return quantile(
                node.left  ,      _A  ,      (node.map_left[start - 1] if start else 0)  ,      node.map_left[end] - 1  ,      )
      else:
            return quantile(
                node.right  ,      index - num_elements_in_left_tree  ,      start - (node.map_left[start - 1] if start else 0)  ,      end - node.map_left[end]  ,      )






def    __lowercase (       _A  ,      _A  ,      _A  ,      _A  ,      _A     )       ->  int:
      if (
          start > end
          or node is None
          or start_num > end_num
          or node.minn > end_num
          or node.maxx < start_num
      ):
            return 0
      if start_num <= node.minn and node.maxx <= end_num:
            return end - start + 1
      SCREAMING_SNAKE_CASE	: Dict					       =				range_counting(
          node.left  ,      (node.map_left[start - 1] if start else 0)  ,      node.map_left[end] - 1  ,      _A  ,      _A  ,      )
      SCREAMING_SNAKE_CASE	: List[str]					       =				range_counting(
          node.right  ,      start - (node.map_left[start - 1] if start else 0)  ,      end - node.map_left[end]  ,      _A  ,      _A  ,      )
      return left + right


if __name__ == "__main__":
  import doctest

  doctest.testmod()




