





class 			__A:

     def __init__(   self,							A   ):





            """simple docstring"""

            _UpperCamelCase														=    val
            # Number of nodes in left subtree
            _UpperCamelCase														=    0
            _UpperCamelCase														=    None
            _UpperCamelCase														=    None
            _UpperCamelCase														=    None



     def 						_UpperCamelCase  (   self,							A   ):





            """simple docstring"""

            assert self.left_tree_size == other.left_tree_size, "Unequal Sizes of Blocks"

            if self.val < other.val:
                   _UpperCamelCase														=    self.right
                   _UpperCamelCase														=    None
                   if self.right:
                          _UpperCamelCase														=    other
                   _UpperCamelCase														=    other
                   _UpperCamelCase														=    self.left_tree_size * 2 + 1
                   return self
            else:
                   _UpperCamelCase														=    other.right
                   _UpperCamelCase														=    None
                   if other.right:
                          _UpperCamelCase														=    self
                   _UpperCamelCase														=    self
                   _UpperCamelCase														=    other.left_tree_size * 2 + 1
                   return other






class 			__A:

     def __init__(   self,							A=None,							A=None,							A=0   ):





            """simple docstring"""

            _UpperCamelCase														=    heap_size
            _UpperCamelCase														=    bottom_root
            _UpperCamelCase														=    min_node

     def 						_UpperCamelCase  (   self,							A   ):





            """simple docstring"""

            if other.size == 0:
                   return None
            if self.size == 0:
                   _UpperCamelCase														=    other.size
                   _UpperCamelCase														=    other.bottom_root
                   _UpperCamelCase														=    other.min_node
                   return None
            # Update size
            _UpperCamelCase														=    self.size + other.size

            # Update min.node
            if self.min_node.val > other.min_node.val:
                   _UpperCamelCase														=    other.min_node
            # Merge

            # Order roots by left_subtree_size
            _UpperCamelCase														=    []
            _UpperCamelCase							,		_UpperCamelCase														=    self.bottom_root, other.bottom_root
            while i or j:
                   if i and ((not j) or i.left_tree_size < j.left_tree_size):
                          combined_roots_list.append((i, True)   )
                          _UpperCamelCase														=    i.parent
                   else:
                          combined_roots_list.append((j, False)   )
                          _UpperCamelCase														=    j.parent
        # Insert links between them
            for i in range(len(A   ) - 1   ):
                   if combined_roots_list[i][1] != combined_roots_list[i + 1][1]:
                          _UpperCamelCase														=    combined_roots_list[i + 1][0]
                          _UpperCamelCase														=    combined_roots_list[i][0]
        # Consecutively merge roots with same left_tree_size
            _UpperCamelCase														=    combined_roots_list[0][0]
            while i.parent:
                   if (
                       (i.left_tree_size == i.parent.left_tree_size) and (not i.parent.parent)
                   ) or (
                       i.left_tree_size == i.parent.left_tree_size
                       and i.left_tree_size != i.parent.parent.left_tree_size
                   ):
                          # Neighbouring Nodes
                          _UpperCamelCase														=    i.left
                          _UpperCamelCase														=    i.parent.parent

                          # Merging trees
                          _UpperCamelCase														=    i.merge_trees(i.parent   )

                          # Updating links
                          _UpperCamelCase														=    previous_node
                          _UpperCamelCase														=    next_node
                          if previous_node:
                                 _UpperCamelCase														=    i
                          if next_node:
                                 _UpperCamelCase														=    i
                   else:
                          _UpperCamelCase														=    i.parent
        # Updating self.bottom_root
            while i.left:
                   _UpperCamelCase														=    i.left
            _UpperCamelCase														=    i

            # Update other
            _UpperCamelCase														=    self.size
            _UpperCamelCase														=    self.bottom_root
            _UpperCamelCase														=    self.min_node

            # Return the merged heap
            return self

     def 						_UpperCamelCase  (   self,							A   ):





            """simple docstring"""

            if self.size == 0:
                   _UpperCamelCase														=    Node(A   )
                   _UpperCamelCase														=    1
                   _UpperCamelCase														=    self.bottom_root
            else:
                   # Create new node
                   _UpperCamelCase														=    Node(A   )

                   # Update size
                   self.size += 1

                   # update min_node
                   if val < self.min_node.val:
                          _UpperCamelCase														=    new_node
                   # Put new_node as a bottom_root in heap
                   _UpperCamelCase														=    new_node
                   _UpperCamelCase														=    self.bottom_root
                   _UpperCamelCase														=    new_node

                   # Consecutively merge roots with same left_tree_size
                   while (
                       self.bottom_root.parent
                       and self.bottom_root.left_tree_size
                       == self.bottom_root.parent.left_tree_size
                   ):
                          # Next node
                          _UpperCamelCase														=    self.bottom_root.parent.parent

                          # Merge
                          _UpperCamelCase														=    self.bottom_root.merge_trees(self.bottom_root.parent   )

                          # Update Links
                          _UpperCamelCase														=    next_node
                          _UpperCamelCase														=    None
                          if next_node:
                                 _UpperCamelCase														=    self.bottom_root

     def 						_UpperCamelCase  (   self   ):





            """simple docstring"""

            return self.min_node.val

     def 						_UpperCamelCase  (   self   ):





            """simple docstring"""

            return self.size == 0

     def 						_UpperCamelCase  (   self   ):





            """simple docstring"""

            _UpperCamelCase														=    self.min_node.val

            # Last element in heap corner case
            if self.size == 1:
                   # Update size
                   _UpperCamelCase														=    0

                   # Update bottom root
                   _UpperCamelCase														=    None

                   # Update min_node
                   _UpperCamelCase														=    None

                   return min_value
            # No right subtree corner case
            # The structure of the tree implies that this should be the bottom root
            # and there is at least one other root
            if self.min_node.right is None:
                   # Update size
                   self.size -= 1

                   # Update bottom root
                   _UpperCamelCase														=    self.bottom_root.parent
                   _UpperCamelCase														=    None

                   # Update min_node
                   _UpperCamelCase														=    self.bottom_root
                   _UpperCamelCase														=    self.bottom_root.parent
                   while i:
                          if i.val < self.min_node.val:
                                 _UpperCamelCase														=    i
                          _UpperCamelCase														=    i.parent
                   return min_value
            # General case
            # Find the BinomialHeap of the right subtree of min_node
            _UpperCamelCase														=    self.min_node.right
            _UpperCamelCase														=    None
            _UpperCamelCase														=    bottom_of_new
            _UpperCamelCase														=    1

            # Size, min_node and bottom_root
            while bottom_of_new.left:
                   _UpperCamelCase														=    size_of_new * 2 + 1
                   _UpperCamelCase														=    bottom_of_new.left
                   if bottom_of_new.val < min_of_new.val:
                          _UpperCamelCase														=    bottom_of_new
        # Corner case of single root on top left path
            if (not self.min_node.left) and (not self.min_node.parent):
                   _UpperCamelCase														=    size_of_new
                   _UpperCamelCase														=    bottom_of_new
                   _UpperCamelCase														=    min_of_new
                   # print("Single root, multiple nodes case")
                   return min_value
            # Remaining cases
            # Construct heap of right subtree
            _UpperCamelCase														=    BinomialHeap(
                bottom_root=A,							min_node=A,							heap_size=A   )

            # Update size
            _UpperCamelCase														=    self.size - 1 - size_of_new

            # Neighbour nodes
            _UpperCamelCase														=    self.min_node.left
            _UpperCamelCase														=    self.min_node.parent

            # Initialize new bottom_root and min_node
            _UpperCamelCase														=    previous_node or next_node
            _UpperCamelCase														=    next_node

            # Update links of previous_node and search below for new min_node and
            # bottom_root
            if previous_node:
                   _UpperCamelCase														=    next_node

                   # Update bottom_root and search for min_node below
                   _UpperCamelCase														=    previous_node
                   _UpperCamelCase														=    previous_node
                   while self.bottom_root.left:
                          _UpperCamelCase														=    self.bottom_root.left
                          if self.bottom_root.val < self.min_node.val:
                                 _UpperCamelCase														=    self.bottom_root
            if next_node:
                   _UpperCamelCase														=    previous_node

                   # Search for new min_node above min_node
                   _UpperCamelCase														=    next_node
                   while i:
                          if i.val < self.min_node.val:
                                 _UpperCamelCase														=    i
                          _UpperCamelCase														=    i.parent
        # Merge heaps
            self.merge_heaps(A   )

            return min_value

     def 						_UpperCamelCase  (   self   ):





            """simple docstring"""

            _UpperCamelCase														=    self.bottom_root
            while top_root.parent:
                   _UpperCamelCase														=    top_root.parent
            # preorder
            _UpperCamelCase														=    []
            self.__traversal(A,							A   )
            return heap_pre_order

     def 						_UpperCamelCase  (   self,							A,							A,							A=0   ):





            """simple docstring"""

            if curr_node:
                   preorder.append((curr_node.val, level)   )
                   self.__traversal(curr_node.left,							A,							level + 1   )
                   self.__traversal(curr_node.right,							A,							level + 1   )
            else:
                   preorder.append(('''#''', level)   )



     def __str__(   self   ):





            """simple docstring"""

            if self.is_empty():
                   return ""
            _UpperCamelCase														=    self.pre_order()

            return "\n".join(('''-''' * level + str(A   )) for value, level in preorder_heap   )


# Unit Tests
if __name__ == "__main__":
       import doctest

       doctest.testmod()













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 SchedulerMixin


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

@dataclass
class 			__A(    __UpperCAmelCase			):
     __A							=							42






class 			__A(    __UpperCAmelCase    ,      __UpperCAmelCase			):
     __A							=							1

     @register_to_config
     def __init__(   self,							A = 40,							A = 0.002,							A = 80.0,							A = 0.5,							A = 1.0,							A = 7.0,							A = True,							):





            """simple docstring"""

            _UpperCamelCase														=    sigma_max

            _UpperCamelCase														=    np.linspace(0,							1,							A   )
            _UpperCamelCase														=    self._convert_to_karras(A   )
            _UpperCamelCase														=    self.sigma_to_t(A   )

            # setable values
            _UpperCamelCase														=    None
            _UpperCamelCase														=    torch.from_numpy(A   )
            _UpperCamelCase														=    torch.from_numpy(A   )
            _UpperCamelCase														=    False
            _UpperCamelCase														=    False

     def 						_UpperCamelCase  (   self,							A,							A=None   ):





            """simple docstring"""

            if schedule_timesteps is None:
                   _UpperCamelCase														=    self.timesteps

            _UpperCamelCase														=    (schedule_timesteps == timestep).nonzero()
            return indices.item()

     def 						_UpperCamelCase  (   self,							A,							A   ):





            """simple docstring"""

            if isinstance(A,							torch.Tensor   ):
                   _UpperCamelCase														=    timestep.to(self.timesteps.device   )
            _UpperCamelCase														=    self.index_for_timestep(A   )
            _UpperCamelCase														=    self.sigmas[step_idx]

            _UpperCamelCase														=    sample / ((sigma**2 + self.config.sigma_data**2) ** 0.5)

            _UpperCamelCase														=    True
            return sample

     def 						_UpperCamelCase  (   self,							A   ):





            """simple docstring"""

            if not isinstance(A,							np.ndarray   ):
                   _UpperCamelCase														=    np.array(A,							dtype=np.floataa   )

            _UpperCamelCase														=    1000 * 0.25 * np.log(sigmas + 1E-4_4   )

            return timesteps

     def 						_UpperCamelCase  (   self,							A = None,							A = None,							A = None,							):





            """simple docstring"""

            if num_inference_steps is None and timesteps is None:
                   raise ValueError('''Exactly one of `num_inference_steps` or `timesteps` must be supplied.'''   )

            if num_inference_steps is not None and timesteps is not None:
                   raise ValueError('''Can only pass one of `num_inference_steps` or `timesteps`.'''   )

            # Follow DDPMScheduler custom timesteps logic
            if timesteps is not None:
                   for i in range(1,							len(A   )   ):
                          if timesteps[i] >= timesteps[i - 1]:
                                 raise ValueError('''`timesteps` must be in descending order.'''   )

                   if timesteps[0] >= self.config.num_train_timesteps:
                          raise ValueError(
                              F'''`timesteps` must start before `self.config.train_timesteps`:'''
                              F''' {self.config.num_train_timesteps}.'''   )

                   _UpperCamelCase														=    np.array(A,							dtype=np.intaa   )
                   _UpperCamelCase														=    True
            else:
                   if num_inference_steps > self.config.num_train_timesteps:
                          raise ValueError(
                              F'''`num_inference_steps`: {num_inference_steps} cannot be larger than `self.config.train_timesteps`:'''
                              F''' {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle'''
                              F''' maximal {self.config.num_train_timesteps} timesteps.'''   )

                   _UpperCamelCase														=    num_inference_steps

                   _UpperCamelCase														=    self.config.num_train_timesteps // self.num_inference_steps
                   _UpperCamelCase														=    (np.arange(0,							A   ) * step_ratio).round()[::-1].copy().astype(np.intaa   )
                   _UpperCamelCase														=    False

            # Map timesteps to Karras sigmas directly for multistep sampling
            # See https://github.com/openai/consistency_models/blob/main/cm/karras_diffusion.py#L675
            _UpperCamelCase														=    self.config.num_train_timesteps
            _UpperCamelCase														=    timesteps[::-1].copy()
            _UpperCamelCase														=    ramp / (num_train_timesteps - 1)
            _UpperCamelCase														=    self._convert_to_karras(A   )
            _UpperCamelCase														=    self.sigma_to_t(A   )

            _UpperCamelCase														=    np.concatenate([sigmas, [self.sigma_min]]   ).astype(np.floataa   )
            _UpperCamelCase														=    torch.from_numpy(A   ).to(device=A   )

            if str(A   ).startswith('''mps'''   ):
                   # mps does not support float64
                   _UpperCamelCase														=    torch.from_numpy(A   ).to(A,							dtype=torch.floataa   )
            else:
                   _UpperCamelCase														=    torch.from_numpy(A   ).to(device=A   )

     def 						_UpperCamelCase  (   self,							A   ):





            """simple docstring"""

            _UpperCamelCase														=    self.config.sigma_min
            _UpperCamelCase														=    self.config.sigma_max

            _UpperCamelCase														=    self.config.rho
            _UpperCamelCase														=    sigma_min ** (1 / rho)
            _UpperCamelCase														=    sigma_max ** (1 / rho)
            _UpperCamelCase														=    (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
            return sigmas

     def 						_UpperCamelCase  (   self,							A   ):





            """simple docstring"""

            _UpperCamelCase														=    self.config.sigma_data

            _UpperCamelCase														=    sigma_data**2 / (sigma**2 + sigma_data**2)
            _UpperCamelCase														=    sigma * sigma_data / (sigma**2 + sigma_data**2) ** 0.5
            return c_skip, c_out

     def 						_UpperCamelCase  (   self,							A   ):





            """simple docstring"""

            _UpperCamelCase														=    self.config.sigma_min
            _UpperCamelCase														=    self.config.sigma_data

            _UpperCamelCase														=    sigma_data**2 / ((sigma - sigma_min) ** 2 + sigma_data**2)
            _UpperCamelCase														=    (sigma - sigma_min) * sigma_data / (sigma**2 + sigma_data**2) ** 0.5
            return c_skip, c_out

     def 						_UpperCamelCase  (   self,							A,							A,							A,							A = None,							A = True,							):





            """simple docstring"""

            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'''
                           F''' `{self.__class__}.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   ):
                   _UpperCamelCase														=    timestep.to(self.timesteps.device   )

            _UpperCamelCase														=    self.config.sigma_min
            _UpperCamelCase														=    self.config.sigma_max

            _UpperCamelCase														=    self.index_for_timestep(A   )

            # sigma_next corresponds to next_t in original implementation
            _UpperCamelCase														=    self.sigmas[step_index]
            if step_index + 1 < self.config.num_train_timesteps:
                   _UpperCamelCase														=    self.sigmas[step_index + 1]
            else:
                   # Set sigma_next to sigma_min
                   _UpperCamelCase														=    self.sigmas[-1]

            # Get scalings for boundary conditions
            _UpperCamelCase							,		_UpperCamelCase														=    self.get_scalings_for_boundary_condition(A   )

            # 1. Denoise model output using boundary conditions
            _UpperCamelCase														=    c_out * model_output + c_skip * sample
            if self.config.clip_denoised:
                   _UpperCamelCase														=    denoised.clamp(-1,							1   )

            # 2. Sample z ~ N(0, s_noise^2 * I)
            # Noise is not used for onestep sampling.
            if len(self.timesteps   ) > 1:
                   _UpperCamelCase														=    randn_tensor(
                       model_output.shape,							dtype=model_output.dtype,							device=model_output.device,							generator=A   )
            else:
                   _UpperCamelCase														=    torch.zeros_like(A   )
            _UpperCamelCase														=    noise * self.config.s_noise

            _UpperCamelCase														=    sigma_next.clamp(min=A,							max=A   )

            # 3. Return noisy sample
            # tau = sigma_hat, eps = sigma_min
            _UpperCamelCase														=    denoised + z * (sigma_hat**2 - sigma_min**2) ** 0.5

            if not return_dict:
                   return (prev_sample,)

            return CMStochasticIterativeSchedulerOutput(prev_sample=A   )

     def 						_UpperCamelCase  (   self,							A,							A,							A,							):





            """simple docstring"""

            _UpperCamelCase														=    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
                   _UpperCamelCase														=    self.timesteps.to(original_samples.device,							dtype=torch.floataa   )
                   _UpperCamelCase														=    timesteps.to(original_samples.device,							dtype=torch.floataa   )
            else:
                   _UpperCamelCase														=    self.timesteps.to(original_samples.device   )
                   _UpperCamelCase														=    timesteps.to(original_samples.device   )

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

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

            _UpperCamelCase														=    original_samples + noise * sigma
            return noisy_samples



     def __len__(   self   ):





            """simple docstring"""

            return self.config.num_train_timesteps






