

'''simple docstring'''






from __future__ import annotations

import unittest
from collections.abc import Iterator
class 	SCREAMING_SNAKE_CASE__			:




    def __init__(					self				,     lowercase__				,     lowercase__			):






          """simple docstring"""






          SCREAMING_SNAKE_CASE_      :			str     =       label
          SCREAMING_SNAKE_CASE_      :			Union[str, Any]     =       parent
          SCREAMING_SNAKE_CASE_      :			Node | None     =       None
          SCREAMING_SNAKE_CASE_      :			Node | None     =       None






class 	SCREAMING_SNAKE_CASE__			:




    def __init__(					self			):






          """simple docstring"""






          SCREAMING_SNAKE_CASE_      :			Node | None     =       None




    def   __lowerCamelCase      (					self			):






          """simple docstring"""






          SCREAMING_SNAKE_CASE_      :			Optional[int]     =       None




    def   __lowerCamelCase      (					self			):






          """simple docstring"""






          return self.root is None




    def   __lowerCamelCase      (					self				,     lowercase__			):






          """simple docstring"""






          SCREAMING_SNAKE_CASE_      :			Optional[int]     =       self._put(self.root				,     lowercase__			)




    def   __lowerCamelCase      (					self				,     lowercase__				,     lowercase__				,     lowercase__ = None			):






          """simple docstring"""






          if node is None:
                SCREAMING_SNAKE_CASE_      :			Optional[Any]     =       Node(lowercase__				,     lowercase__			)
          else:
                if label < node.label:
                      SCREAMING_SNAKE_CASE_      :			Union[str, Any]     =       self._put(node.left				,     lowercase__				,     lowercase__			)
                elif label > node.label:
                      SCREAMING_SNAKE_CASE_      :			List[Any]     =       self._put(node.right				,     lowercase__				,     lowercase__			)
                else:
                      SCREAMING_SNAKE_CASE_      :			str     =       F"Node with label {label} already exists"
                      raise Exception(lowercase__			)

          return node




    def   __lowerCamelCase      (					self				,     lowercase__			):






          """simple docstring"""






          return self._search(self.root				,     lowercase__			)




    def   __lowerCamelCase      (					self				,     lowercase__				,     lowercase__			):






          """simple docstring"""






          if node is None:
                SCREAMING_SNAKE_CASE_      :			Dict     =       F"Node with label {label} does not exist"
                raise Exception(lowercase__			)
          else:
                if label < node.label:
                      SCREAMING_SNAKE_CASE_      :			Optional[int]     =       self._search(node.left				,     lowercase__			)
                elif label > node.label:
                      SCREAMING_SNAKE_CASE_      :			str     =       self._search(node.right				,     lowercase__			)

          return node




    def   __lowerCamelCase      (					self				,     lowercase__			):






          """simple docstring"""






          SCREAMING_SNAKE_CASE_      :			str     =       self.search(lowercase__			)
          if node.right and node.left:
                SCREAMING_SNAKE_CASE_      :			Dict     =       self._get_lowest_node(node.right			)
                SCREAMING_SNAKE_CASE_      :			str     =       node.left
                SCREAMING_SNAKE_CASE_      :			str     =       node.right
                SCREAMING_SNAKE_CASE_      :			Dict     =       lowest_node
                if node.right:
                      SCREAMING_SNAKE_CASE_      :			Any     =       lowest_node
                self._reassign_nodes(lowercase__				,     lowercase__			)
          elif not node.right and node.left:
                self._reassign_nodes(lowercase__				,     node.left			)
          elif node.right and not node.left:
                self._reassign_nodes(lowercase__				,     node.right			)
          else:
                self._reassign_nodes(lowercase__				,     lowercase__			)




    def   __lowerCamelCase      (					self				,     lowercase__				,     lowercase__			):






          """simple docstring"""






          if new_children:
                SCREAMING_SNAKE_CASE_      :			str     =       node.parent

          if node.parent:
                if node.parent.right == node:
                      SCREAMING_SNAKE_CASE_      :			str     =       new_children
                else:
                      SCREAMING_SNAKE_CASE_      :			Optional[Any]     =       new_children
          else:
                SCREAMING_SNAKE_CASE_      :			Tuple     =       new_children




    def   __lowerCamelCase      (					self				,     lowercase__			):






          """simple docstring"""






          if node.left:
                SCREAMING_SNAKE_CASE_      :			List[Any]     =       self._get_lowest_node(node.left			)
          else:
                SCREAMING_SNAKE_CASE_      :			Tuple     =       node
                self._reassign_nodes(lowercase__				,     node.right			)

          return lowest_node




    def   __lowerCamelCase      (					self				,     lowercase__			):






          """simple docstring"""






          try:
                self.search(lowercase__			)
                return True
          except Exception:
                return False




    def   __lowerCamelCase      (					self			):






          """simple docstring"""






          if self.root is None:
                raise Exception("Binary search tree is empty"			)

          SCREAMING_SNAKE_CASE_      :			Union[str, Any]     =       self.root
          while node.right is not None:
                SCREAMING_SNAKE_CASE_      :			Dict     =       node.right

          return node.label




    def   __lowerCamelCase      (					self			):






          """simple docstring"""






          if self.root is None:
                raise Exception("Binary search tree is empty"			)

          SCREAMING_SNAKE_CASE_      :			Any     =       self.root
          while node.left is not None:
                SCREAMING_SNAKE_CASE_      :			List[str]     =       node.left

          return node.label




    def   __lowerCamelCase      (					self			):






          """simple docstring"""






          return self._inorder_traversal(self.root			)




    def   __lowerCamelCase      (					self				,     lowercase__			):






          """simple docstring"""






          if node is not None:
                yield from self._inorder_traversal(node.left			)
                yield node
                yield from self._inorder_traversal(node.right			)




    def   __lowerCamelCase      (					self			):






          """simple docstring"""






          return self._preorder_traversal(self.root			)







    def   __lowerCamelCase      (					self				,     lowercase__			):






          """simple docstring"""






          if node is not None:
                yield node
                yield from self._preorder_traversal(node.left			)
                yield from self._preorder_traversal(node.right			)






class 	SCREAMING_SNAKE_CASE__			(				unittest.TestCase      ):




    @staticmethod
    def   __lowerCamelCase      (					):






          """simple docstring"""






          SCREAMING_SNAKE_CASE_      :			List[str]     =       BinarySearchTree()
          t.put(8			)
          t.put(3			)
          t.put(6			)
          t.put(1			)
          t.put(10			)
          t.put(14			)
          t.put(13			)
          t.put(4			)
          t.put(7			)
          t.put(5			)

          return t




    def   __lowerCamelCase      (					self			):






          """simple docstring"""






          SCREAMING_SNAKE_CASE_      :			Any     =       BinarySearchTree()
          assert t.is_empty()

          t.put(8			)
          assert t.root is not None
          assert t.root.parent is None
          assert t.root.label == 8

          t.put(10			)
          assert t.root.right is not None
          assert t.root.right.parent == t.root
          assert t.root.right.label == 10

          t.put(3			)
          assert t.root.left is not None
          assert t.root.left.parent == t.root
          assert t.root.left.label == 3

          t.put(6			)
          assert t.root.left.right is not None
          assert t.root.left.right.parent == t.root.left
          assert t.root.left.right.label == 6

          t.put(1			)
          assert t.root.left.left is not None
          assert t.root.left.left.parent == t.root.left
          assert t.root.left.left.label == 1

          with self.assertRaises(lowercase__			):  # noqa: B017
                t.put(1			)




    def   __lowerCamelCase      (					self			):






          """simple docstring"""






          SCREAMING_SNAKE_CASE_      :			List[Any]     =       self._get_binary_search_tree()

          SCREAMING_SNAKE_CASE_      :			str     =       t.search(6			)
          assert node.label == 6

          SCREAMING_SNAKE_CASE_      :			int     =       t.search(13			)
          assert node.label == 13

          with self.assertRaises(lowercase__			):  # noqa: B017
                t.search(2			)




    def   __lowerCamelCase      (					self			):






          """simple docstring"""






          SCREAMING_SNAKE_CASE_      :			List[str]     =       self._get_binary_search_tree()

          t.remove(13			)
          assert t.root is not None
          assert t.root.right is not None
          assert t.root.right.right is not None
          assert t.root.right.right.right is None
          assert t.root.right.right.left is None

          t.remove(7			)
          assert t.root.left is not None
          assert t.root.left.right is not None
          assert t.root.left.right.left is not None
          assert t.root.left.right.right is None
          assert t.root.left.right.left.label == 4

          t.remove(6			)
          assert t.root.left.left is not None
          assert t.root.left.right.right is not None
          assert t.root.left.left.label == 1
          assert t.root.left.right.label == 4
          assert t.root.left.right.right.label == 5
          assert t.root.left.right.left is None
          assert t.root.left.left.parent == t.root.left
          assert t.root.left.right.parent == t.root.left

          t.remove(3			)
          assert t.root is not None
          assert t.root.left.label == 4
          assert t.root.left.right.label == 5
          assert t.root.left.left.label == 1
          assert t.root.left.parent == t.root
          assert t.root.left.left.parent == t.root.left
          assert t.root.left.right.parent == t.root.left

          t.remove(4			)
          assert t.root.left is not None
          assert t.root.left.left is not None
          assert t.root.left.label == 5
          assert t.root.left.right is None
          assert t.root.left.left.label == 1
          assert t.root.left.parent == t.root
          assert t.root.left.left.parent == t.root.left




    def   __lowerCamelCase      (					self			):






          """simple docstring"""






          SCREAMING_SNAKE_CASE_      :			Dict     =       self._get_binary_search_tree()

          t.remove(3			)
          assert t.root is not None
          assert t.root.left is not None
          assert t.root.left.left is not None
          assert t.root.left.right is not None
          assert t.root.left.right.left is not None
          assert t.root.left.right.right is not None
          assert t.root.left.label == 4
          assert t.root.left.right.label == 6
          assert t.root.left.left.label == 1
          assert t.root.left.right.right.label == 7
          assert t.root.left.right.left.label == 5
          assert t.root.left.parent == t.root
          assert t.root.left.right.parent == t.root.left
          assert t.root.left.left.parent == t.root.left
          assert t.root.left.right.left.parent == t.root.left.right




    def   __lowerCamelCase      (					self			):






          """simple docstring"""






          SCREAMING_SNAKE_CASE_      :			Any     =       self._get_binary_search_tree()
          t.empty()
          assert t.root is None




    def   __lowerCamelCase      (					self			):






          """simple docstring"""






          SCREAMING_SNAKE_CASE_      :			Optional[Any]     =       self._get_binary_search_tree()
          assert not t.is_empty()

          t.empty()
          assert t.is_empty()




    def   __lowerCamelCase      (					self			):






          """simple docstring"""






          SCREAMING_SNAKE_CASE_      :			str     =       self._get_binary_search_tree()

          assert t.exists(6			)
          assert not t.exists(-1			)




    def   __lowerCamelCase      (					self			):






          """simple docstring"""






          SCREAMING_SNAKE_CASE_      :			Tuple     =       self._get_binary_search_tree()

          assert t.get_max_label() == 14

          t.empty()
          with self.assertRaises(lowercase__			):  # noqa: B017
                t.get_max_label()




    def   __lowerCamelCase      (					self			):






          """simple docstring"""






          SCREAMING_SNAKE_CASE_      :			Tuple     =       self._get_binary_search_tree()

          assert t.get_min_label() == 1

          t.empty()
          with self.assertRaises(lowercase__			):  # noqa: B017
                t.get_min_label()




    def   __lowerCamelCase      (					self			):






          """simple docstring"""






          SCREAMING_SNAKE_CASE_      :			List[str]     =       self._get_binary_search_tree()

          SCREAMING_SNAKE_CASE_      :			Dict     =       [i.label for i in t.inorder_traversal()]
          assert inorder_traversal_nodes == [1, 3, 4, 5, 6, 7, 8, 10, 13, 14]







    def   __lowerCamelCase      (					self			):






          """simple docstring"""






          SCREAMING_SNAKE_CASE_      :			int     =       self._get_binary_search_tree()

          SCREAMING_SNAKE_CASE_      :			Any     =       [i.label for i in t.preorder_traversal()]
          assert preorder_traversal_nodes == [8, 3, 1, 6, 4, 5, 7, 10, 14, 13]






def 					__lowerCamelCase			(      )							->   None:
      """simple docstring"""

      SCREAMING_SNAKE_CASE_      :			int     =       BinarySearchTree()
      t.put(8    )
      t.put(3    )
      t.put(6    )
      t.put(1    )
      t.put(1_0    )
      t.put(1_4    )
      t.put(1_3    )
      t.put(4    )
      t.put(7    )
      t.put(5    )

      print(
          "\n            8\n           / \\\n          3   10\n         / \\    \\\n        1   6    14\n           / \\   /\n          4   7 13\n           \\\n            5\n        "    )

      print("Label 6 exists:"  ,  t.exists(6    )    )
      print("Label 13 exists:"  ,  t.exists(1_3    )    )
      print("Label -1 exists:"  ,  t.exists(-1    )    )
      print("Label 12 exists:"  ,  t.exists(1_2    )    )

      # Prints all the elements of the list in inorder traversal
      SCREAMING_SNAKE_CASE_      :			Dict     =       [i.label for i in t.inorder_traversal()]
      print("Inorder traversal:"  ,  SCREAMING_SNAKE_CASE_    )

      # Prints all the elements of the list in preorder traversal
      SCREAMING_SNAKE_CASE_      :			Union[str, Any]     =       [i.label for i in t.preorder_traversal()]
      print("Preorder traversal:"  ,  SCREAMING_SNAKE_CASE_    )

      print("Max. label:"  ,  t.get_max_label()    )
      print("Min. label:"  ,  t.get_min_label()    )

      # Delete elements
      print("\nDeleting elements 13, 10, 8, 3, 6, 14"    )
      print(
          "\n          4\n         / \\\n        1   7\n             \\\n              5\n        "    )
      t.remove(1_3    )
      t.remove(1_0    )
      t.remove(8    )
      t.remove(3    )
      t.remove(6    )
      t.remove(1_4    )

      # Prints all the elements of the list in inorder traversal after delete
      SCREAMING_SNAKE_CASE_      :			Optional[int]     =       [i.label for i in t.inorder_traversal()]
      print("Inorder traversal after delete:"  ,  SCREAMING_SNAKE_CASE_    )

      # Prints all the elements of the list in preorder traversal after delete
      SCREAMING_SNAKE_CASE_      :			Optional[int]     =       [i.label for i in t.preorder_traversal()]
      print("Preorder traversal after delete:"  ,  SCREAMING_SNAKE_CASE_    )

      print("Max. label:"  ,  t.get_max_label()    )
      print("Min. label:"  ,  t.get_min_label()    )


if __name__ == "__main__":
      binary_search_tree_example()




'''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


snake_case_       =       logging.get_logger(__name__)  # pylint: disable=invalid-name
@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerAncestralDiscrete
class 	SCREAMING_SNAKE_CASE__			(				_UpperCAmelCase      ):
    _A			    =							42
    _A			    =							None






def 					__lowerCamelCase			(      SCREAMING_SNAKE_CASE_     :	Any  ,  SCREAMING_SNAKE_CASE_     :	int=0.999  ,  SCREAMING_SNAKE_CASE_     :	Optional[Any]="cosine"  ,  )							->   Optional[int]:
      """simple docstring"""

      if alpha_transform_type == "cosine":

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

      elif alpha_transform_type == "exp":

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

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

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





class 	SCREAMING_SNAKE_CASE__			(				_UpperCAmelCase,_UpperCAmelCase      ):
    _A			    =							[e.name for e in KarrasDiffusionSchedulers]
    _A			    =							1




    @register_to_config
    def __init__(					self				,     lowercase__ = 1000				,     lowercase__ = 0.0001				,     lowercase__ = 0.02				,     lowercase__ = "linear"				,     lowercase__ = None				,     lowercase__ = "epsilon"				,     lowercase__ = "linspace"				,     lowercase__ = 0				,     ):






          """simple docstring"""






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

          SCREAMING_SNAKE_CASE_      :			Any     =       1.0 - self.betas
          SCREAMING_SNAKE_CASE_      :			Tuple     =       torch.cumprod(self.alphas				,     dim=0			)

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

          # setable values
          SCREAMING_SNAKE_CASE_      :			Optional[int]     =       None
          SCREAMING_SNAKE_CASE_      :			str     =       np.linspace(0				,     num_train_timesteps - 1				,     lowercase__				,     dtype=lowercase__			)[::-1].copy()
          SCREAMING_SNAKE_CASE_      :			Optional[Any]     =       torch.from_numpy(lowercase__			)
          SCREAMING_SNAKE_CASE_      :			int     =       False




    @property
    def   __lowerCamelCase      (					self			):






          """simple docstring"""






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

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




    def   __lowerCamelCase      (					self				,     lowercase__				,     lowercase__			):






          """simple docstring"""






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




    def   __lowerCamelCase      (					self				,     lowercase__				,     lowercase__ = None			):






          """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_      :			Dict     =       np.linspace(0				,     self.config.num_train_timesteps - 1				,     lowercase__				,     dtype=lowercase__			)[
                    ::-1
                ].copy()
          elif self.config.timestep_spacing == "leading":
                SCREAMING_SNAKE_CASE_      :			Dict     =       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_      :			Union[str, Any]     =       (np.arange(0				,     lowercase__			) * step_ratio).round()[::-1].copy().astype(lowercase__			)
                timesteps += self.config.steps_offset
          elif self.config.timestep_spacing == "trailing":
                SCREAMING_SNAKE_CASE_      :			Optional[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_      :			Any     =       (np.arange(self.config.num_train_timesteps				,     0				,     -step_ratio			)).round().copy().astype(lowercase__			)
                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_      :			int     =       np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5			)
          SCREAMING_SNAKE_CASE_      :			Any     =       np.interp(lowercase__				,     np.arange(0				,     len(lowercase__			)			)				,     lowercase__			)
          SCREAMING_SNAKE_CASE_      :			List[str]     =       np.concatenate([sigmas, [0.0]]			).astype(np.floataa			)
          SCREAMING_SNAKE_CASE_      :			Any     =       torch.from_numpy(lowercase__			).to(device=lowercase__			)
          if str(lowercase__			).startswith("mps"			):
                # mps does not support float64
                SCREAMING_SNAKE_CASE_      :			List[Any]     =       torch.from_numpy(lowercase__			).to(lowercase__				,     dtype=torch.floataa			)
          else:
                SCREAMING_SNAKE_CASE_      :			Tuple     =       torch.from_numpy(lowercase__			).to(device=lowercase__			)




    def   __lowerCamelCase      (					self				,     lowercase__				,     lowercase__				,     lowercase__				,     lowercase__ = None				,     lowercase__ = True				,     ):






          """simple docstring"""






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

          SCREAMING_SNAKE_CASE_      :			Tuple     =       (self.timesteps == timestep).nonzero().item()
          SCREAMING_SNAKE_CASE_      :			str     =       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_      :			Any     =       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_      :			Optional[int]     =       self.sigmas[step_index]
          SCREAMING_SNAKE_CASE_      :			Any     =       self.sigmas[step_index + 1]
          SCREAMING_SNAKE_CASE_      :			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_      :			List[Any]     =       (sample - pred_original_sample) / sigma

          SCREAMING_SNAKE_CASE_      :			List[Any]     =       sigma_down - sigma

          SCREAMING_SNAKE_CASE_      :			Optional[Any]     =       sample + derivative * dt

          SCREAMING_SNAKE_CASE_      :			Dict     =       model_output.device
          SCREAMING_SNAKE_CASE_      :			int     =       randn_tensor(model_output.shape				,     dtype=model_output.dtype				,     device=lowercase__				,     generator=lowercase__			)

          SCREAMING_SNAKE_CASE_      :			List[Any]     =       prev_sample + noise * sigma_up

          if not return_dict:
                return (prev_sample,)

          return EulerAncestralDiscreteSchedulerOutput(
              prev_sample=lowercase__				,     pred_original_sample=lowercase__			)




    def   __lowerCamelCase      (					self				,     lowercase__				,     lowercase__				,     lowercase__				,     ):






          """simple docstring"""






          SCREAMING_SNAKE_CASE_      :			str     =       self.sigmas.to(device=original_samples.device				,     dtype=original_samples.dtype			)
          if original_samples.device.type == "mps" and torch.is_floating_point(lowercase__			):
                # mps does not support float64
                SCREAMING_SNAKE_CASE_      :			Optional[int]     =       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_      :			Optional[int]     =       self.timesteps.to(original_samples.device			)
                SCREAMING_SNAKE_CASE_      :			Optional[Any]     =       timesteps.to(original_samples.device			)

          SCREAMING_SNAKE_CASE_      :			Union[str, Any]     =       [(schedule_timesteps == t).nonzero().item() for t in timesteps]

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

          SCREAMING_SNAKE_CASE_      :			Dict     =       original_samples + noise * sigma
          return noisy_samples







    def __len__(					self			):






          """simple docstring"""






          return self.config.num_train_timesteps

