





import math
from collections import defaultdict
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import randn_tensor
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput




def 			__UpperCamelCase  (_SCREAMING_SNAKE_CASE		,						_SCREAMING_SNAKE_CASE=0.9_9_9		,						_SCREAMING_SNAKE_CASE="cosine"		,						)				->   Dict:
  if alpha_transform_type == "cosine":

    def alpha_bar_fn(_SCREAMING_SNAKE_CASE		):
      return math.cos((t + 0.0_0_8) / 1.0_0_8 * math.pi / 2		) ** 2

  elif alpha_transform_type == "exp":

    def alpha_bar_fn(_SCREAMING_SNAKE_CASE		):
      return math.exp(t * -1_2.0		)

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

  lowercase__				=  []
  for i in range(lowerCamelCase_		):
    lowercase__				=  i / num_diffusion_timesteps
    lowercase__				=  (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[int] 					=       [e.name for e in KarrasDiffusionSchedulers]
   _UpperCamelCase    :		Dict 					=       2


   @register_to_config
   def __init__(    self			:				List[Any]			,     a			:				Tuple = 1_000			,     a			:				Tuple = 0.00085			,     a			:				Optional[Any] = 0.012			,     a			:				Union[str, Any] = "linear"			,     a			:				str = None			,     a			:				Any = "epsilon"			,     a			:				Union[str, Any] = "linspace"			,     a			:				Tuple = 0			,     )->   Dict:





     """simple docstring"""







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

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

     #  set all values
     self.set_timesteps(_lowerCamelCase			,     _lowerCamelCase			,     _lowerCamelCase       )


   def        SCREAMING_SNAKE_CASE_							(    self			:				int			,     a			:				Any			,     a			:				Union[str, Any]=None       )->   Any:





     """simple docstring"""







     if schedule_timesteps is None:
       lowercase__				=  self.timesteps

     lowercase__				=  (schedule_timesteps == timestep).nonzero()

     # The sigma index that is taken for the **very** first `step`
     # is always the second index (or the last index if there is only 1)
     # This way we can ensure we don't accidentally skip a sigma in
     # case we start in the middle of the denoising schedule (e.g. for image-to-image)
     if len(self._index_counter       ) == 0:
       lowercase__				=  1 if len(_lowerCamelCase       ) > 1 else 0
     else:
       lowercase__				=  timestep.cpu().item() if torch.is_tensor(_lowerCamelCase       ) else timestep
       lowercase__				=  self._index_counter[timestep_int]

     return indices[pos].item()


   @property
   def        SCREAMING_SNAKE_CASE_							(    self			:				Dict       )->   Optional[Any]:





     """simple docstring"""







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

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


   def        SCREAMING_SNAKE_CASE_							(    self			:				int			,     a			:				List[Any]			,     a			:				List[str]			,     )->   torch.FloatTensor:





     """simple docstring"""







     lowercase__				=  self.index_for_timestep(_lowerCamelCase       )

     if self.state_in_first_order:
       lowercase__				=  self.sigmas[step_index]
     else:
       lowercase__				=  self.sigmas_interpol[step_index - 1]

     lowercase__				=  sample / ((sigma**2 + 1) ** 0.5)
     return sample


   def        SCREAMING_SNAKE_CASE_							(    self			:				List[Any]			,     a			:				List[Any]			,     a			:				Union[str, Any] = None			,     a			:				Optional[int] = None			,     )->   List[Any]:





     """simple docstring"""







     lowercase__				=  num_inference_steps

     lowercase__				=  num_train_timesteps or self.config.num_train_timesteps

     # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
     if self.config.timestep_spacing == "linspace":
       lowercase__				=  np.linspace(0			,     num_train_timesteps - 1			,     _lowerCamelCase			,     dtype=_lowerCamelCase       )[::-1].copy()
     elif self.config.timestep_spacing == "leading":
       lowercase__				=  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
       lowercase__				=  (np.arange(0			,     _lowerCamelCase       ) * step_ratio).round()[::-1].copy().astype(_lowerCamelCase       )
       timesteps += self.config.steps_offset
     elif self.config.timestep_spacing == "trailing":
       lowercase__				=  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
       lowercase__				=  (np.arange(_lowerCamelCase			,     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'."""       )

     lowercase__				=  np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5       )
     lowercase__				=  torch.from_numpy(np.log(_lowerCamelCase       )       ).to(_lowerCamelCase       )

     lowercase__				=  np.interp(_lowerCamelCase			,     np.arange(0			,     len(_lowerCamelCase       )       )			,     _lowerCamelCase       )
     lowercase__				=  np.concatenate([sigmas, [0.0]]       ).astype(np.floataa       )
     lowercase__				=  torch.from_numpy(_lowerCamelCase       ).to(device=_lowerCamelCase       )

     # compute up and down sigmas
     lowercase__				=  sigmas.roll(-1       )
     lowercase__				=  0.0
     lowercase__				=  (sigmas_next**2 * (sigmas**2 - sigmas_next**2) / sigmas**2) ** 0.5
     lowercase__				=  (sigmas_next**2 - sigmas_up**2) ** 0.5
     lowercase__				=  0.0

     # compute interpolated sigmas
     lowercase__				=  sigmas.log().lerp(sigmas_down.log()			,     0.5       ).exp()
     lowercase__				=  0.0

     # set sigmas
     lowercase__				=  torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2       ), sigmas[-1:]]       )
     lowercase__				=  torch.cat(
         [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2       ), sigmas_interpol[-1:]]       )
     lowercase__				=  torch.cat([sigmas_up[:1], sigmas_up[1:].repeat_interleave(2       ), sigmas_up[-1:]]       )
     lowercase__				=  torch.cat([sigmas_down[:1], sigmas_down[1:].repeat_interleave(2       ), sigmas_down[-1:]]       )

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

     lowercase__				=  self.sigma_to_t(_lowerCamelCase       ).to(_lowerCamelCase			,     dtype=timesteps.dtype       )
     lowercase__				=  torch.stack((timesteps_interpol[:-2, None], timesteps[1:, None])			,     dim=-1       ).flatten()

     lowercase__				=  torch.cat([timesteps[:1], interleaved_timesteps]       )

     lowercase__				=  None

     # for exp beta schedules, such as the one for `pipeline_shap_e.py`
     # we need an index counter
     lowercase__				=  defaultdict(_lowerCamelCase       )


   def        SCREAMING_SNAKE_CASE_							(    self			:				int			,     a			:				int       )->   Tuple:





     """simple docstring"""







     lowercase__				=  sigma.log()

     # get distribution
     lowercase__				=  log_sigma - self.log_sigmas[:, None]

     # get sigmas range
     lowercase__				=  dists.ge(0       ).cumsum(dim=0       ).argmax(dim=0       ).clamp(max=self.log_sigmas.shape[0] - 2       )
     lowercase__				=  low_idx + 1

     lowercase__				=  self.log_sigmas[low_idx]
     lowercase__				=  self.log_sigmas[high_idx]

     # interpolate sigmas
     lowercase__				=  (low - log_sigma) / (low - high)
     lowercase__				=  w.clamp(0			,     1       )

     # transform interpolation to time range
     lowercase__				=  (1 - w) * low_idx + w * high_idx
     lowercase__				=  t.view(sigma.shape       )
     return t


   @property
   def        SCREAMING_SNAKE_CASE_							(    self			:				Optional[int]       )->   Optional[Any]:





     """simple docstring"""







     return self.sample is None


   def        SCREAMING_SNAKE_CASE_							(    self			:				Any			,     a			:				Tuple			,     a			:				List[Any]			,     a			:				List[str]			,     a			:				List[str] = None			,     a			:				Any = True			,     )->   Union[SchedulerOutput, Tuple]:





     """simple docstring"""







     lowercase__				=  self.index_for_timestep(_lowerCamelCase       )

     # advance index counter by 1
     lowercase__				=  timestep.cpu().item() if torch.is_tensor(_lowerCamelCase       ) else timestep
     self._index_counter[timestep_int] += 1

     if self.state_in_first_order:
       lowercase__				=  self.sigmas[step_index]
       lowercase__				=  self.sigmas_interpol[step_index]
       lowercase__				=  self.sigmas_up[step_index]
       lowercase__				=  self.sigmas_down[step_index - 1]
     else:
       # 2nd order / KPDM2's method
       lowercase__				=  self.sigmas[step_index - 1]
       lowercase__				=  self.sigmas_interpol[step_index - 1]
       lowercase__				=  self.sigmas_up[step_index - 1]
       lowercase__				=  self.sigmas_down[step_index - 1]

     # currently only gamma=0 is supported. This usually works best anyways.
     # We can support gamma in the future but then need to scale the timestep before
     # passing it to the model which requires a change in API
     lowercase__				=  0
     lowercase__				=  sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

     lowercase__				=  model_output.device
     lowercase__				=  randn_tensor(model_output.shape			,     dtype=model_output.dtype			,     device=_lowerCamelCase			,     generator=_lowerCamelCase       )

     # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
     if self.config.prediction_type == "epsilon":
       lowercase__				=  sigma_hat if self.state_in_first_order else sigma_interpol
       lowercase__				=  sample - sigma_input * model_output
     elif self.config.prediction_type == "v_prediction":
       lowercase__				=  sigma_hat if self.state_in_first_order else sigma_interpol
       lowercase__				=  model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
           sample / (sigma_input**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`"""       )

     if self.state_in_first_order:
       # 2. Convert to an ODE derivative for 1st order
       lowercase__				=  (sample - pred_original_sample) / sigma_hat
       # 3. delta timestep
       lowercase__				=  sigma_interpol - sigma_hat

       # store for 2nd order step
       lowercase__				=  sample
       lowercase__				=  dt
       lowercase__				=  sample + derivative * dt
     else:
       # DPM-Solver-2
       # 2. Convert to an ODE derivative for 2nd order
       lowercase__				=  (sample - pred_original_sample) / sigma_interpol
       # 3. delta timestep
       lowercase__				=  sigma_down - sigma_hat

       lowercase__				=  self.sample
       lowercase__				=  None

       lowercase__				=  sample + derivative * dt
       lowercase__				=  prev_sample + noise * sigma_up

     if not return_dict:
       return (prev_sample,)

     return SchedulerOutput(prev_sample=_lowerCamelCase       )


   def        SCREAMING_SNAKE_CASE_							(    self			:				Tuple			,     a			:				List[str]			,     a			:				int			,     a			:				Tuple			,     )->   torch.FloatTensor:





     """simple docstring"""







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

     lowercase__				=  [self.index_for_timestep(_lowerCamelCase			,     _lowerCamelCase       ) for t in timesteps]

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

     lowercase__				=  original_samples + noise * sigma
     return noisy_samples


   def __len__(    self			:				Dict       )->   Any:





     """simple docstring"""







     return self.config.num_train_timesteps









'''simple docstring'''



class 							__lowercase				:







	'''simple docstring'''

	def __init__(self   ,_lowerCamelCase       )							->							Optional[Any]:







				'''simple docstring'''





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


	def   _UpperCAmelCase   (self   ,_lowerCamelCase       )							->							Tuple:







				'''simple docstring'''





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

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






class 							__lowercase				:







	'''simple docstring'''

	def __init__(self   ,_lowerCamelCase=None   ,_lowerCamelCase=None   ,_lowerCamelCase=0       )							->							int:







				'''simple docstring'''





				__lowercase   =							heap_size
				__lowercase   =							bottom_root
				__lowercase   =							min_node


	def   _UpperCAmelCase   (self   ,_lowerCamelCase       )							->							Tuple:







				'''simple docstring'''





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

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

				# Order roots by left_subtree_size
				__lowercase   =							[]
				__lowercase  ,						__lowercase   =							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)       )
										__lowercase   =							i.parent
							else:
										combined_roots_list.append((j, False)       )
										__lowercase   =							j.parent
        # Insert links between them
				for i in range(len(_lowerCamelCase       ) - 1       ):
							if combined_roots_list[i][1] != combined_roots_list[i + 1][1]:
										__lowercase   =							combined_roots_list[i + 1][0]
										__lowercase   =							combined_roots_list[i][0]
        # Consecutively merge roots with same left_tree_size
				__lowercase   =							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
										__lowercase   =							i.left
										__lowercase   =							i.parent.parent

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

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

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

				# Return the merged heap
				return self


	def   _UpperCAmelCase   (self   ,_lowerCamelCase       )							->							Dict:







				'''simple docstring'''





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

							# Update size
							self.size += 1

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

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

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


	def   _UpperCAmelCase   (self       )							->							Union[str, Any]:







				'''simple docstring'''





				return self.min_node.val


	def   _UpperCAmelCase   (self       )							->							List[Any]:







				'''simple docstring'''





				return self.size == 0


	def   _UpperCAmelCase   (self       )							->							Union[str, Any]:







				'''simple docstring'''





				__lowercase   =							self.min_node.val

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

							# Update bottom root
							__lowercase   =							None

							# Update min_node
							__lowercase   =							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
							__lowercase   =							self.bottom_root.parent
							__lowercase   =							None

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

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

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

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

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

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

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

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

				return min_value


	def   _UpperCAmelCase   (self       )							->							str:







				'''simple docstring'''





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


	def   _UpperCAmelCase   (self   ,_lowerCamelCase   ,_lowerCamelCase   ,_lowerCamelCase=0       )							->							str:







				'''simple docstring'''





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


	def __str__(self       )							->							List[str]:







				'''simple docstring'''





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

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


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

	doctest.testmod()





