'''simple docstring'''





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






@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerAncestralDiscrete
class 							_SCREAMING_SNAKE_CASE(   lowerCAmelCase__	):
   UpperCamelCase_				:						int 			=   42
   UpperCamelCase_				:						int 			=   None







def 	UpperCAmelCase       (		lowerCAmelCase_						,      lowerCAmelCase_=0.9_99						,      lowerCAmelCase_="cosine"						,      )	->	Union[str, Any]:
     if alpha_transform_type == "cosine":

          def alpha_bar_fn(lowerCAmelCase_       ):
               return math.cos((t + 0.0_08) / 1.0_08 * math.pi / 2       ) ** 2

     elif alpha_transform_type == "exp":

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

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

     a  :    Any				=						[]
     for i in range(lowerCAmelCase_       ):
          a  :    Any				=						i / num_diffusion_timesteps
          a  :    Optional[Any]				=						(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(   lowerCAmelCase__       ,      lowerCAmelCase__	):
   UpperCamelCase_				:						Optional[Any] 			=   [e.name for e in KarrasDiffusionSchedulers]
   UpperCamelCase_				:						Any 			=   1
   @register_to_config
   def __init__(    self							,     lowerCAmelCase_ = 10_00							,     lowerCAmelCase_ = 0.00_01							,     lowerCAmelCase_ = 0.02							,     lowerCAmelCase_ = "linear"							,     lowerCAmelCase_ = None							,     lowerCAmelCase_ = "epsilon"							,     lowerCAmelCase_ = "linspace"							,     lowerCAmelCase_ = 0							,     )	->Tuple:

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

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

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

        # setable values
        a  :    int				=						None
        a  :    Any				=						np.linspace(0							,     num_train_timesteps - 1							,     _lowerCamelCase							,     dtype=_lowerCamelCase    )[::-1].copy()
        a  :    int				=						torch.from_numpy(_lowerCamelCase    )
        a  :    Optional[Any]				=						False
   @property
   def _lowercase(    self    )	->Dict:

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

        return (self.sigmas.max() ** 2 + 1) ** 0.5
   def _lowercase(    self							,     lowerCAmelCase_							,     lowerCAmelCase_    )	->str:

        if isinstance(_lowerCamelCase							,     torch.Tensor    ):
             a  :    Optional[int]				=						timestep.to(self.timesteps.device    )
        a  :    List[str]				=						(self.timesteps == timestep).nonzero().item()
        a  :    int				=						self.sigmas[step_index]
        a  :    List[Any]				=						sample / ((sigma**2 + 1) ** 0.5)
        a  :    int				=						True
        return sample
   def _lowercase(    self							,     lowerCAmelCase_							,     lowerCAmelCase_ = None    )	->List[Any]:
        a  :    Dict				=						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  :    Union[str, Any]				=						np.linspace(0							,     self.config.num_train_timesteps - 1							,     _lowerCamelCase							,     dtype=_lowerCamelCase    )[
                 ::-1
             ].copy()
        elif self.config.timestep_spacing == "leading":
             a  :    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
             a  :    Tuple				=						(np.arange(0							,     _lowerCamelCase    ) * step_ratio).round()[::-1].copy().astype(_lowerCamelCase    )
             timesteps += self.config.steps_offset
        elif self.config.timestep_spacing == "trailing":
             a  :    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
             a  :    int				=						(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'."""    )

        a  :    Any				=						np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5    )
        a  :    Dict				=						np.interp(_lowerCamelCase							,     np.arange(0							,     len(_lowerCamelCase    )    )							,     _lowerCamelCase    )
        a  :    Union[str, Any]				=						np.concatenate([sigmas, [0.0]]    ).astype(np.floataa    )
        a  :    Tuple				=						torch.from_numpy(_lowerCamelCase    ).to(device=_lowerCamelCase    )
        if str(_lowerCamelCase    ).startswith('''mps'''    ):
             # mps does not support float64
             a  :    List[Any]				=						torch.from_numpy(_lowerCamelCase    ).to(_lowerCamelCase							,     dtype=torch.floataa    )
        else:
             a  :    List[Any]				=						torch.from_numpy(_lowerCamelCase    ).to(device=_lowerCamelCase    )
   def _lowercase(    self							,     lowerCAmelCase_							,     lowerCAmelCase_							,     lowerCAmelCase_							,     lowerCAmelCase_ = None							,     lowerCAmelCase_ = True							,     )	->Any:

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

        a  :    Dict				=						(self.timesteps == timestep).nonzero().item()
        a  :    Optional[Any]				=						self.sigmas[step_index]

        # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
        if self.config.prediction_type == "epsilon":
             a  :    Tuple				=						sample - sigma * model_output
        elif self.config.prediction_type == "v_prediction":
             # * c_out + input * c_skip
             a  :    Tuple				=						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  :    Dict				=						self.sigmas[step_index]
        a  :    Optional[int]				=						self.sigmas[step_index + 1]
        a  :    List[Any]				=						(sigma_to**2 * (sigma_from**2 - sigma_to**2) / sigma_from**2) ** 0.5
        a  :    List[Any]				=						(sigma_to**2 - sigma_up**2) ** 0.5

        # 2. Convert to an ODE derivative
        a  :    Union[str, Any]				=						(sample - pred_original_sample) / sigma

        a  :    Optional[Any]				=						sigma_down - sigma

        a  :    Tuple				=						sample + derivative * dt

        a  :    Dict				=						model_output.device
        a  :    Optional[Any]				=						randn_tensor(model_output.shape							,     dtype=model_output.dtype							,     device=_lowerCamelCase							,     generator=_lowerCamelCase    )

        a  :    Optional[Any]				=						prev_sample + noise * sigma_up

        if not return_dict:
             return (prev_sample,)

        return EulerAncestralDiscreteSchedulerOutput(
            prev_sample=_lowerCamelCase							,     pred_original_sample=_lowerCamelCase    )
   def _lowercase(    self							,     lowerCAmelCase_							,     lowerCAmelCase_							,     lowerCAmelCase_							,     )	->Optional[Any]:
        a  :    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
             a  :    Any				=						self.timesteps.to(original_samples.device							,     dtype=torch.floataa    )
             a  :    str				=						timesteps.to(original_samples.device							,     dtype=torch.floataa    )
        else:
             a  :    List[str]				=						self.timesteps.to(original_samples.device    )
             a  :    Dict				=						timesteps.to(original_samples.device    )

        a  :    Optional[int]				=						[(schedule_timesteps == t).nonzero().item() for t in timesteps]

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

        a  :    Union[str, Any]				=						original_samples + noise * sigma
        return noisy_samples


   def __len__(    self    )	->Any:
        return self.config.num_train_timesteps
from __future__ import annotations

UpperCAmelCase							   =      [2, 1, 4, 5, 6, 0, 8, 9, 1, 2, 0, 6, 4, 2, 0, 6, 5, 3, 2, 7]






class 							_SCREAMING_SNAKE_CASE:
   def __init__(    self							,     lowerCAmelCase_    )	->None:
        a  :    int				=						-1
        a  :    int				=						-1
        a  :    list[int]				=						[-1] * length
        a  :    Node | None				=						None
        a  :    Node | None				=						None


   def __repr__(    self    )	->str:
        return F"""Node(min_value={self.minn} max_value={self.maxx})"""







def 	UpperCAmelCase       (		lowerCAmelCase_       )	->	Node | None:
     a  :    Dict				=						Node(len(lowerCAmelCase_       )       )
     a			,							a  :    Tuple				=						min(lowerCAmelCase_       ), max(lowerCAmelCase_       )
     # Leaf node case where the node contains only one unique value
     if root.minn == root.maxx:
          return root
     a  :    Optional[Any]				=						(root.minn + root.maxx) // 2

     a  :    list[int]				=						[]
     a  :    list[int]				=						[]

     for index, num in enumerate(lowerCAmelCase_       ):
          if num <= pivot:
               left_arr.append(lowerCAmelCase_       )
          else:
               right_arr.append(lowerCAmelCase_       )
          a  :    int				=						len(lowerCAmelCase_       )
     a  :    List[str]				=						build_tree(lowerCAmelCase_       )
     a  :    List[str]				=						build_tree(lowerCAmelCase_       )
     return root







def 	UpperCAmelCase       (		lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_       )	->	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
     a  :    List[Any]				=						(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						,      lowerCAmelCase_						,      node.map_left[index] - 1       )
     else:
          # go to the right subtree and map index to the right subtree
          return rank_till_index(node.right						,      lowerCAmelCase_						,      index - node.map_left[index]       )







def 	UpperCAmelCase       (		lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_       )	->	int:
     if start > end:
          return 0
     a  :    Optional[Any]				=						rank_till_index(lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_       )
     a  :    Any				=						rank_till_index(lowerCAmelCase_						,      lowerCAmelCase_						,      start - 1       )
     return rank_till_end - rank_before_start







def 	UpperCAmelCase       (		lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_       )	->	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]
     a  :    Optional[int]				=						node.map_left[end] - (
         node.map_left[start - 1] if start else 0
     )
     if num_elements_in_left_tree > index:
          return quantile(
              node.left						,      lowerCAmelCase_						,      (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 	UpperCAmelCase       (		lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_       )	->	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
     a  :    Tuple				=						range_counting(
         node.left						,      (node.map_left[start - 1] if start else 0)						,      node.map_left[end] - 1						,      lowerCAmelCase_						,      lowerCAmelCase_						,      )
     a  :    int				=						range_counting(
         node.right						,      start - (node.map_left[start - 1] if start else 0)						,      end - node.map_left[end]						,      lowerCAmelCase_						,      lowerCAmelCase_						,      )
     return left + right


if __name__ == "__main__":
  import doctest

  doctest.testmod()