



"""simple docstring"""


import math







class  A_     :



						"""simple docstring"""






						def __init__(   self					:Any  ,    lowercase_					:Optional[Any]   )							->     Tuple:
												UpperCAmelCase			 =					len(lowercase_   )
												UpperCAmelCase			 =					[0] * (
												    4 * self.N
												)  # approximate the overall size of segment tree with array N
												self.build(1  ,    0  ,    self.N - 1   )






						def       UpperCAmelCase__	(   self					:List[Any]  ,    lowercase_					:Optional[Any]   )							->     Union[str, Any]:
												return idx * 2






						def       UpperCAmelCase__	(   self					:Dict  ,    lowercase_					:Optional[Any]   )							->     int:
												return idx * 2 + 1






						def       UpperCAmelCase__	(   self					:str  ,    lowercase_					:Union[str, Any]  ,    lowercase_					:Tuple  ,    lowercase_					:Tuple   )							->     Dict:  # noqa: E741
												if l == r:
																		UpperCAmelCase			 =					A[l]
												else:
																		UpperCAmelCase			 =					(l + r) // 2
																		self.build(self.left(lowercase_   )  ,    lowercase_  ,    lowercase_   )
																		self.build(self.right(lowercase_   )  ,    mid + 1  ,    lowercase_   )
																		UpperCAmelCase			 =					max(self.st[self.left(lowercase_   )]  ,    self.st[self.right(lowercase_   )]   )






						def       UpperCAmelCase__	(   self					:Union[str, Any]  ,    lowercase_					:Union[str, Any]  ,    lowercase_					:Optional[Any]  ,    lowercase_					:Optional[Any]   )							->     Any:
												return self.update_recursive(1  ,    0  ,    self.N - 1  ,    a - 1  ,    b - 1  ,    lowercase_   )






						def       UpperCAmelCase__	(   self					:Any  ,    lowercase_					:Optional[Any]  ,    lowercase_					:int  ,    lowercase_					:List[Any]  ,    lowercase_					:List[Any]  ,    lowercase_					:List[str]  ,    lowercase_					:int   )							->     Dict:  # noqa: E741
												if r < a or l > b:
																		return True
												if l == r:
																		UpperCAmelCase			 =					val
																		return True
												UpperCAmelCase			 =					(l + r) // 2
												self.update_recursive(self.left(lowercase_   )  ,    lowercase_  ,    lowercase_  ,    lowercase_  ,    lowercase_  ,    lowercase_   )
												self.update_recursive(self.right(lowercase_   )  ,    mid + 1  ,    lowercase_  ,    lowercase_  ,    lowercase_  ,    lowercase_   )
												UpperCAmelCase			 =					max(self.st[self.left(lowercase_   )]  ,    self.st[self.right(lowercase_   )]   )
												return True






						def       UpperCAmelCase__	(   self					:List[str]  ,    lowercase_					:Tuple  ,    lowercase_					:List[str]   )							->     Dict:
												return self.query_recursive(1  ,    0  ,    self.N - 1  ,    a - 1  ,    b - 1   )






						def       UpperCAmelCase__	(   self					:Union[str, Any]  ,    lowercase_					:Tuple  ,    lowercase_					:Optional[int]  ,    lowercase_					:List[str]  ,    lowercase_					:int  ,    lowercase_					:List[Any]   )							->     Dict:  # noqa: E741
												if r < a or l > b:
																		return -math.inf
												if l >= a and r <= b:
																		return self.st[idx]
												UpperCAmelCase			 =					(l + r) // 2
												UpperCAmelCase			 =					self.query_recursive(self.left(lowercase_   )  ,    lowercase_  ,    lowercase_  ,    lowercase_  ,    lowercase_   )
												UpperCAmelCase			 =					self.query_recursive(self.right(lowercase_   )  ,    mid + 1  ,    lowercase_  ,    lowercase_  ,    lowercase_   )
												return max(lowercase_  ,    lowercase_   )






						def       UpperCAmelCase__	(   self					:str   )							->     Any:
												UpperCAmelCase			 =					[]
												for i in range(1  ,    N + 1   ):
																		show_list += [self.query(lowercase_  ,    lowercase_   )]
												print(lowercase_   )


if __name__ == "__main__":
				snake_case_								=			[1, 2, -4, 7, 3, -5, 6, 11, -20, 9, 14, 15, 5, 2, -8]
				snake_case_								=			15
				snake_case_								=			SegmentTree(A)
				print(segt.query(4, 6))
				print(segt.query(7, 11))
				print(segt.query(7, 12))
				segt.update(1, 3, 111)
				print(segt.query(1, 15))
				segt.update(7, 8, 235)
				segt.show_data()








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


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







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


  """simple docstring"""
  SCREAMING_SNAKE_CASE__					:			torch.FloatTensor
  SCREAMING_SNAKE_CASE__					:			Optional[torch.FloatTensor]					    =   None





def 				__a							(       __A			,							__A=0.999			,							__A="cosine"			,							):
    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__         =    []
    for i in range(__A						):
        SCREAMING_SNAKE_CASE__         =    i / num_diffusion_timesteps
        SCREAMING_SNAKE_CASE__         =    (i + 1) / num_diffusion_timesteps
        betas.append(min(1 - alpha_bar_fn(__A						) / alpha_bar_fn(__A						)			,							__A						)						)
    return torch.tensor(__A			,							dtype=torch.floataa						)







class  UpperCamelCase_      (	_snake_case		,  _snake_case      ):


  """simple docstring"""
  SCREAMING_SNAKE_CASE__					:			Union[str, Any]					    =   [e.name for e in KarrasDiffusionSchedulers]
  SCREAMING_SNAKE_CASE__					:			List[Any]					    =   1



  @register_to_config
  def __init__(						self     :					Tuple  ,	A_     :					int = 1000  ,	A_     :					float = 0.0_001  ,	A_     :					float = 0.02  ,	A_     :					str = "linear"  ,	A_     :					Optional[Union[np.ndarray, List[float]]] = None  ,	A_     :					str = "epsilon"  ,	A_     :					str = "linspace"  ,	A_     :					int = 0  ,	)       ->			Optional[Any]:
      if trained_betas is not None:
          SCREAMING_SNAKE_CASE__         =    torch.tensor(A_  ,	dtype=torch.floataa						)
      elif beta_schedule == "linear":
          SCREAMING_SNAKE_CASE__         =    torch.linspace(A_  ,	A_  ,	A_  ,	dtype=torch.floataa						)
      elif beta_schedule == "scaled_linear":
          # this schedule is very specific to the latent diffusion model.
          SCREAMING_SNAKE_CASE__         =    (
              torch.linspace(beta_start**0.5  ,	beta_end**0.5  ,	A_  ,	dtype=torch.floataa						) ** 2
          )
      elif beta_schedule == "squaredcos_cap_v2":
          # Glide cosine schedule
          SCREAMING_SNAKE_CASE__         =    betas_for_alpha_bar(A_						)
      else:
          raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}"						)

      SCREAMING_SNAKE_CASE__         =    1.0 - self.betas
      SCREAMING_SNAKE_CASE__         =    torch.cumprod(self.alphas  ,	dim=0						)

      SCREAMING_SNAKE_CASE__         =    np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5						)
      SCREAMING_SNAKE_CASE__         =    np.concatenate([sigmas[::-1], [0.0]]						).astype(np.floataa						)
      SCREAMING_SNAKE_CASE__         =    torch.from_numpy(A_						)

      # setable values
      SCREAMING_SNAKE_CASE__         =    None
      SCREAMING_SNAKE_CASE__         =    np.linspace(0  ,	num_train_timesteps - 1  ,	A_  ,	dtype=A_						)[::-1].copy()
      SCREAMING_SNAKE_CASE__         =    torch.from_numpy(A_						)
      SCREAMING_SNAKE_CASE__         =    False



  @property
  def   _UpperCamelCase     (						self     :					Union[str, Any]						)       ->			Dict:
      # 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   _UpperCamelCase     (						self     :					str  ,	A_     :					torch.FloatTensor  ,	A_     :					Union[float, torch.FloatTensor]						)       ->			torch.FloatTensor:
      if isinstance(A_  ,	torch.Tensor						):
          SCREAMING_SNAKE_CASE__         =    timestep.to(self.timesteps.device						)
      SCREAMING_SNAKE_CASE__         =    (self.timesteps == timestep).nonzero().item()
      SCREAMING_SNAKE_CASE__         =    self.sigmas[step_index]
      SCREAMING_SNAKE_CASE__         =    sample / ((sigma**2 + 1) ** 0.5)
      SCREAMING_SNAKE_CASE__         =    True
      return sample



  def   _UpperCamelCase     (						self     :					List[Any]  ,	A_     :					int  ,	A_     :					Union[str, torch.device] = None						)       ->			Optional[int]:
      SCREAMING_SNAKE_CASE__         =    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__         =    np.linspace(0  ,	self.config.num_train_timesteps - 1  ,	A_  ,	dtype=A_						)[
              ::-1
          ].copy()
      elif self.config.timestep_spacing == "leading":
          SCREAMING_SNAKE_CASE__         =    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__         =    (np.arange(0  ,	A_						) * step_ratio).round()[::-1].copy().astype(A_						)
          timesteps += self.config.steps_offset
      elif self.config.timestep_spacing == "trailing":
          SCREAMING_SNAKE_CASE__         =    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__         =    (np.arange(self.config.num_train_timesteps  ,	0  ,	-step_ratio						)).round().copy().astype(A_						)
          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__         =    np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5						)
      SCREAMING_SNAKE_CASE__         =    np.interp(A_  ,	np.arange(0  ,	len(A_						)						)  ,	A_						)
      SCREAMING_SNAKE_CASE__         =    np.concatenate([sigmas, [0.0]]						).astype(np.floataa						)
      SCREAMING_SNAKE_CASE__         =    torch.from_numpy(A_						).to(device=A_						)
      if str(A_						).startswith("mps"						):
          # mps does not support float64
          SCREAMING_SNAKE_CASE__         =    torch.from_numpy(A_						).to(A_  ,	dtype=torch.floataa						)
      else:
          SCREAMING_SNAKE_CASE__         =    torch.from_numpy(A_						).to(device=A_						)



  def   _UpperCamelCase     (						self     :					Tuple  ,	A_     :					torch.FloatTensor  ,	A_     :					Union[float, torch.FloatTensor]  ,	A_     :					torch.FloatTensor  ,	A_     :					Optional[torch.Generator] = None  ,	A_     :					bool = True  ,	)       ->			Union[EulerAncestralDiscreteSchedulerOutput, Tuple]:

      if (
          isinstance(A_  ,	A_						)
          or isinstance(A_  ,	torch.IntTensor						)
          or isinstance(A_  ,	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(A_  ,	torch.Tensor						):
          SCREAMING_SNAKE_CASE__         =    timestep.to(self.timesteps.device						)

      SCREAMING_SNAKE_CASE__         =    (self.timesteps == timestep).nonzero().item()
      SCREAMING_SNAKE_CASE__         =    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__         =    sample - sigma * model_output
      elif self.config.prediction_type == "v_prediction":
          # * c_out + input * c_skip
          SCREAMING_SNAKE_CASE__         =    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__         =    self.sigmas[step_index]
      SCREAMING_SNAKE_CASE__         =    self.sigmas[step_index + 1]
      SCREAMING_SNAKE_CASE__         =    (sigma_to**2 * (sigma_from**2 - sigma_to**2) / sigma_from**2) ** 0.5
      SCREAMING_SNAKE_CASE__         =    (sigma_to**2 - sigma_up**2) ** 0.5

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

      SCREAMING_SNAKE_CASE__         =    sigma_down - sigma

      SCREAMING_SNAKE_CASE__         =    sample + derivative * dt

      SCREAMING_SNAKE_CASE__         =    model_output.device
      SCREAMING_SNAKE_CASE__         =    randn_tensor(model_output.shape  ,	dtype=model_output.dtype  ,	device=A_  ,	generator=A_						)

      SCREAMING_SNAKE_CASE__         =    prev_sample + noise * sigma_up

      if not return_dict:
          return (prev_sample,)

      return EulerAncestralDiscreteSchedulerOutput(
          prev_sample=A_  ,	pred_original_sample=A_						)



  def   _UpperCamelCase     (						self     :					Tuple  ,	A_     :					torch.FloatTensor  ,	A_     :					torch.FloatTensor  ,	A_     :					torch.FloatTensor  ,	)       ->			torch.FloatTensor:
      # Make sure sigmas and timesteps have the same device and dtype as original_samples
      SCREAMING_SNAKE_CASE__         =    self.sigmas.to(device=original_samples.device  ,	dtype=original_samples.dtype						)
      if original_samples.device.type == "mps" and torch.is_floating_point(A_						):
          # mps does not support float64
          SCREAMING_SNAKE_CASE__         =    self.timesteps.to(original_samples.device  ,	dtype=torch.floataa						)
          SCREAMING_SNAKE_CASE__         =    timesteps.to(original_samples.device  ,	dtype=torch.floataa						)
      else:
          SCREAMING_SNAKE_CASE__         =    self.timesteps.to(original_samples.device						)
          SCREAMING_SNAKE_CASE__         =    timesteps.to(original_samples.device						)

      SCREAMING_SNAKE_CASE__         =    [(schedule_timesteps == t).nonzero().item() for t in timesteps]

      SCREAMING_SNAKE_CASE__         =    sigmas[step_indices].flatten()
      while len(sigma.shape						) < len(original_samples.shape						):
          SCREAMING_SNAKE_CASE__         =    sigma.unsqueeze(-1						)

      SCREAMING_SNAKE_CASE__         =    original_samples + noise * sigma
      return noisy_samples







  def __len__(						self     :					List[Any]						)       ->			Tuple:
      return self.config.num_train_timesteps


