




import math
import warnings
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch
from scipy import integrate

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin




@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->LMSDiscrete
class 			a__       (					lowerCAmelCase__      ):
     a		:			torch.FloatTensor
     a		:			Optional[torch.FloatTensor]							=	None







def 					SCREAMING_SNAKE_CASE							(   __UpperCamelCase		,					__UpperCamelCase=0.999		,					__UpperCamelCase="cosine"		,					)			->     str:
     if alpha_transform_type == "cosine":

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

     elif alpha_transform_type == "exp":

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

     else:
          raise ValueError(f'''Unsupported alpha_tranform_type: {alpha_transform_type}''')

     a      =      []
     for i in range(lowerCamelCase_):
          a      =      i / num_diffusion_timesteps
          a      =      (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 			a__       (					lowerCAmelCase__   ,					lowerCAmelCase__      ):
     a		:			Dict							=	[e.name for e in KarrasDiffusionSchedulers]
     a		:			Dict							=	1







     @register_to_config
     def __init__(	self  ,		A = 1000  ,		A = 0.0_0_0_1  ,		A = 0.0_2  ,		A = "linear"  ,		A = None  ,		A = False  ,		A = "epsilon"  ,		A = "linspace"  ,		A = 0  ,		)  ->    Union[str, Any]:



          '''simple docstring'''



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

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

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

          # setable values
          a      =      None
          a      =      use_karras_sigmas
          self.set_timesteps(_lowerCamelCase  ,		_lowerCamelCase )
          a      =      []
          a      =      False







     @property
     def 			lowerCAmelCase_				(	self )  ->    Union[str, Any]:



          '''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  ,		A  ,		A )  ->    torch.FloatTensor:



          '''simple docstring'''



          if isinstance(_lowerCamelCase  ,		torch.Tensor ):
               a      =      timestep.to(self.timesteps.device )
          a      =      (self.timesteps == timestep).nonzero().item()
          a      =      self.sigmas[step_index]
          a      =      sample / ((sigma**2 + 1) ** 0.5)
          a      =      True
          return sample







     def 			lowerCAmelCase_				(	self  ,		A  ,		A  ,		A )  ->    Tuple:



          '''simple docstring'''



          def lms_derivative(A ):
               a      =      1.0
               for k in range(_lowerCamelCase ):
                    if current_order == k:
                         continue
                    prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
               return prod

          a      =      integrate.quad(_lowerCamelCase  ,		self.sigmas[t]  ,		self.sigmas[t + 1]  ,		epsrel=1e-4 )[0]

          return integrated_coeff







     def 			lowerCAmelCase_				(	self  ,		A  ,		A = None )  ->    List[str]:



          '''simple docstring'''



          a      =      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":
               a      =      np.linspace(0  ,		self.config.num_train_timesteps - 1  ,		_lowerCamelCase  ,		dtype=_lowerCamelCase )[
                   ::-1
               ].copy()
          elif self.config.timestep_spacing == "leading":
               a      =      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
               a      =      (np.arange(0  ,		_lowerCamelCase ) * step_ratio).round()[::-1].copy().astype(_lowerCamelCase )
               timesteps += self.config.steps_offset
          elif self.config.timestep_spacing == "trailing":
               a      =      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
               a      =      (np.arange(self.config.num_train_timesteps  ,		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\'.''' )

          a      =      np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5 )
          a      =      np.log(_lowerCamelCase )
          a      =      np.interp(_lowerCamelCase  ,		np.arange(0  ,		len(_lowerCamelCase ) )  ,		_lowerCamelCase )

          if self.use_karras_sigmas:
               a      =      self._convert_to_karras(in_sigmas=_lowerCamelCase )
               a      =      np.array([self._sigma_to_t(_lowerCamelCase  ,		_lowerCamelCase ) for sigma in sigmas] )

          a      =      np.concatenate([sigmas, [0.0]] ).astype(np.floataa )

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

          a      =      []







     def 			lowerCAmelCase_				(	self  ,		A  ,		A )  ->    Any:



          '''simple docstring'''



          a      =      np.log(_lowerCamelCase )

          # get distribution
          a      =      log_sigma - log_sigmas[:, np.newaxis]

          # get sigmas range
          a      =      np.cumsum((dists >= 0)  ,		axis=0 ).argmax(axis=0 ).clip(max=log_sigmas.shape[0] - 2 )
          a      =      low_idx + 1

          a      =      log_sigmas[low_idx]
          a      =      log_sigmas[high_idx]

          # interpolate sigmas
          a      =      (low - log_sigma) / (low - high)
          a      =      np.clip(_lowerCamelCase  ,		0  ,		1 )

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







     def 			lowerCAmelCase_				(	self  ,		A )  ->    torch.FloatTensor:



          '''simple docstring'''



          a      =      in_sigmas[-1].item()
          a      =      in_sigmas[0].item()

          a      =      7.0  # 7.0 is the value used in the paper
          a      =      np.linspace(0  ,		1  ,		self.num_inference_steps )
          a      =      sigma_min ** (1 / rho)
          a      =      sigma_max ** (1 / rho)
          a      =      (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
          return sigmas







     def 			lowerCAmelCase_				(	self  ,		A  ,		A  ,		A  ,		A = 4  ,		A = True  ,		)  ->    Union[LMSDiscreteSchedulerOutput, Tuple]:



          '''simple docstring'''



          if not self.is_scale_input_called:
               warnings.warn(
                   "The `scale_model_input` function should be called before `step` to ensure correct denoising. "
                   "See `StableDiffusionPipeline` for a usage example." )

          if isinstance(_lowerCamelCase  ,		torch.Tensor ):
               a      =      timestep.to(self.timesteps.device )
          a      =      (self.timesteps == timestep).nonzero().item()
          a      =      self.sigmas[step_index]

          # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
          if self.config.prediction_type == "epsilon":
               a      =      sample - sigma * model_output
          elif self.config.prediction_type == "v_prediction":
               # * c_out + input * c_skip
               a      =      model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
          elif self.config.prediction_type == "sample":
               a      =      model_output
          else:
               raise ValueError(
                   F'''prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`''' )

          # 2. Convert to an ODE derivative
          a      =      (sample - pred_original_sample) / sigma
          self.derivatives.append(_lowerCamelCase )
          if len(self.derivatives ) > order:
               self.derivatives.pop(0 )

          # 3. Compute linear multistep coefficients
          a      =      min(step_index + 1  ,		_lowerCamelCase )
          a      =      [self.get_lms_coefficient(_lowerCamelCase  ,		_lowerCamelCase  ,		_lowerCamelCase ) for curr_order in range(_lowerCamelCase )]

          # 4. Compute previous sample based on the derivatives path
          a      =      sample + sum(
              coeff * derivative for coeff, derivative in zip(_lowerCamelCase  ,		reversed(self.derivatives ) ) )

          if not return_dict:
               return (prev_sample,)

          return LMSDiscreteSchedulerOutput(prev_sample=_lowerCamelCase  ,		pred_original_sample=_lowerCamelCase )







     def 			lowerCAmelCase_				(	self  ,		A  ,		A  ,		A  ,		)  ->    torch.FloatTensor:



          '''simple docstring'''



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

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

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

          a      =      original_samples + noise * sigma
          return noisy_samples







     def __len__(	self )  ->    Optional[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()





