





'''simple docstring'''



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       _lowerCAmelCase  ( lowerCamelCase_	:     List[Any]						,				lowerCamelCase_	:     Tuple=0.9_99						,				lowerCamelCase_	:     List[str]="cosine"						,				):
			if alpha_transform_type == "cosine":

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

			elif alpha_transform_type == "exp":

						def alpha_bar_fn(lowerCamelCase_	:     List[Any] ):
									return math.exp(t * -12.0 )

			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 							__lowercase				(					lowerCAmelCase__       ,					lowerCAmelCase__  ):







	'''simple docstring'''

	a			: Optional[int]      =				[e.name for e in KarrasDiffusionSchedulers]
	a			: Dict      =				2


	@register_to_config
	def __init__(self   ,_lowerCamelCase = 1000   ,_lowerCamelCase = 0.0_0_0_8_5   ,_lowerCamelCase = 0.0_1_2   ,_lowerCamelCase = "linear"   ,_lowerCamelCase = None   ,_lowerCamelCase = "epsilon"   ,_lowerCamelCase = "linspace"   ,_lowerCamelCase = 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   _UpperCAmelCase   (self   ,_lowerCamelCase   ,_lowerCamelCase=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   _UpperCAmelCase   (self       )							->							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   _UpperCAmelCase   (self   ,_lowerCamelCase   ,_lowerCamelCase   ,)							->							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   _UpperCAmelCase   (self   ,_lowerCamelCase   ,_lowerCamelCase = None   ,_lowerCamelCase = 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   _UpperCAmelCase   (self   ,_lowerCamelCase       )							->							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   _UpperCAmelCase   (self       )							->							Optional[Any]:







				'''simple docstring'''





				return self.sample is None


	def   _UpperCAmelCase   (self   ,_lowerCamelCase   ,_lowerCamelCase   ,_lowerCamelCase   ,_lowerCamelCase = None   ,_lowerCamelCase = 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   _UpperCAmelCase   (self   ,_lowerCamelCase   ,_lowerCamelCase   ,_lowerCamelCase   ,)							->							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       )							->							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()





