



from __future__ import annotations

from sys import maxsize
from typing import Generic, TypeVar

A__    :    List[str]        =   TypeVar('''T''')


def      UpperCamelCase(    __UpperCamelCase				:						List[Any]					):
		return (position - 1) // 2


def      UpperCamelCase(    __UpperCamelCase				:						Optional[Any]					):
		return (2 * position) + 1


def      UpperCamelCase(    __UpperCamelCase				:						Dict					):
		return (2 * position) + 2



class 							__snake_case		(	Generic[T]		):




							def __init__(			self	:			Any):
									lowerCAmelCase_     :	List[Any]							   =					[]
									lowerCAmelCase_     :	Optional[int]							   =					{}
									lowerCAmelCase_     :	Optional[Any]							   =					0




							def __len__(			self	:			Union[str, Any]):
									return self.elements




							def __repr__(			self	:			Optional[Any]):
									return str(self.heap)




							def   UpperCAmelCase__     (			self	:			List[str]):
									# Check if the priority queue is empty
									return self.elements == 0




							def   UpperCAmelCase__     (			self	:			List[Any]							,							A_	:			Dict							,							A_	:			Dict):
									# Add an element with given priority to the queue
									self.heap.append((elem, weight))
									lowerCAmelCase_     :	Optional[int]							   =					self.elements
									self.elements += 1
									self._bubble_up(_UpperCAmelCase)




							def   UpperCAmelCase__     (			self	:			Optional[Any]):
									# Remove and return the element with lowest weight (highest priority)
									if self.elements > 1:
											self._swap_nodes(0							,							self.elements - 1)
									lowerCAmelCase_   ,    lowerCAmelCase_     :	Union[str, Any]							   =					self.heap.pop()
									del self.position_map[elem]
									self.elements -= 1
									if self.elements > 0:
											lowerCAmelCase_   ,    lowerCAmelCase_     :	Optional[Any]							   =					self.heap[0]
											self._bubble_down(_UpperCAmelCase)
									return elem




							def   UpperCAmelCase__     (			self	:			Optional[Any]							,							A_	:			List[str]							,							A_	:			Dict):
									# Update the weight of the given key
									lowerCAmelCase_     :	Union[str, Any]							   =					self.position_map[elem]
									lowerCAmelCase_     :	str							   =					(elem, weight)
									if position > 0:
											lowerCAmelCase_     :	Any							   =					get_parent_position(_UpperCAmelCase)
											lowerCAmelCase_   ,    lowerCAmelCase_     :	Optional[Any]							   =					self.heap[parent_position]
											if parent_weight > weight:
													self._bubble_up(_UpperCAmelCase)
											else:
													self._bubble_down(_UpperCAmelCase)
									else:
											self._bubble_down(_UpperCAmelCase)




							def   UpperCAmelCase__     (			self	:			List[Any]							,							A_	:			List[str]):
									# Place a node at the proper position (upward movement) [to be used internally
									# only]
									lowerCAmelCase_     :	Tuple							   =					self.position_map[elem]
									if curr_pos == 0:
											return None
									lowerCAmelCase_     :	Optional[int]							   =					get_parent_position(_UpperCAmelCase)
									lowerCAmelCase_   ,    lowerCAmelCase_     :	Any							   =					self.heap[curr_pos]
									lowerCAmelCase_   ,    lowerCAmelCase_     :	Dict							   =					self.heap[parent_position]
									if parent_weight > weight:
											self._swap_nodes(_UpperCAmelCase							,							_UpperCAmelCase)
											return self._bubble_up(_UpperCAmelCase)
									return None




							def   UpperCAmelCase__     (			self	:			Optional[int]							,							A_	:			Union[str, Any]):
									# Place a node at the proper position (downward movement) [to be used
									# internally only]
									lowerCAmelCase_     :	int							   =					self.position_map[elem]
									lowerCAmelCase_   ,    lowerCAmelCase_     :	Optional[Any]							   =					self.heap[curr_pos]
									lowerCAmelCase_     :	Optional[Any]							   =					get_child_left_position(_UpperCAmelCase)
									lowerCAmelCase_     :	Dict							   =					get_child_right_position(_UpperCAmelCase)
									if child_left_position < self.elements and child_right_position < self.elements:
											lowerCAmelCase_   ,    lowerCAmelCase_     :	Union[str, Any]							   =					self.heap[child_left_position]
											lowerCAmelCase_   ,    lowerCAmelCase_     :	str							   =					self.heap[child_right_position]
											if child_right_weight < child_left_weight and child_right_weight < weight:
													self._swap_nodes(_UpperCAmelCase							,							_UpperCAmelCase)
													return self._bubble_down(_UpperCAmelCase)
									if child_left_position < self.elements:
											lowerCAmelCase_   ,    lowerCAmelCase_     :	int							   =					self.heap[child_left_position]
											if child_left_weight < weight:
													self._swap_nodes(_UpperCAmelCase							,							_UpperCAmelCase)
													return self._bubble_down(_UpperCAmelCase)
									else:
											return None
									if child_right_position < self.elements:
											lowerCAmelCase_   ,    lowerCAmelCase_     :	Any							   =					self.heap[child_right_position]
											if child_right_weight < weight:
													self._swap_nodes(_UpperCAmelCase							,							_UpperCAmelCase)
													return self._bubble_down(_UpperCAmelCase)
									return None







							def   UpperCAmelCase__     (			self	:			Any							,							A_	:			List[Any]							,							A_	:			int):
									# Swap the nodes at the given positions
									lowerCAmelCase_     :	Any							   =					self.heap[nodea_pos][0]
									lowerCAmelCase_     :	Union[str, Any]							   =					self.heap[nodea_pos][0]
									lowerCAmelCase_   ,    lowerCAmelCase_     :	Optional[int]							   =					(
									    self.heap[nodea_pos],
									    self.heap[nodea_pos],
									)
									lowerCAmelCase_     :	Tuple							   =					nodea_pos
									lowerCAmelCase_     :	Any							   =					nodea_pos





class 							__snake_case		(	Generic[T]		):




							def __init__(			self	:			int):
									lowerCAmelCase_     :	int							   =					{}
									lowerCAmelCase_     :	int							   =					0




							def __repr__(			self	:			Tuple):
									return str(self.connections)




							def __len__(			self	:			Tuple):
									return self.nodes




							def   UpperCAmelCase__     (			self	:			Any							,							A_	:			str):
									# Add a node in the graph if it is not in the graph
									if node not in self.connections:
											lowerCAmelCase_     :	Optional[int]							   =					{}
											self.nodes += 1







							def   UpperCAmelCase__     (			self	:			List[Any]							,							A_	:			Optional[Any]							,							A_	:			Tuple							,							A_	:			List[Any]):
									# Add an edge between 2 nodes in the graph
									self.add_node(_UpperCAmelCase)
									self.add_node(_UpperCAmelCase)
									lowerCAmelCase_     :	Tuple							   =					weight
									lowerCAmelCase_     :	List[Any]							   =					weight





def      UpperCamelCase(    __UpperCamelCase				:						Any	,):
		lowerCAmelCase_     :	Union[str, Any]							   =					{node: maxsize for node in graph.connections}
		lowerCAmelCase_     :	Dict							   =					{node: None for node in graph.connections}

		lowerCAmelCase_     :	Union[str, Any]							   =					MinPriorityQueue()
		for node, weight in dist.items():
				priority_queue.push(__lowercase	,__lowercase					)

		if priority_queue.is_empty():
				return dist, parent

		# initialization
		lowerCAmelCase_     :	List[str]							   =					priority_queue.extract_min()
		lowerCAmelCase_     :	List[str]							   =					0
		for neighbour in graph.connections[node]:
				if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
						lowerCAmelCase_     :	int							   =					dist[node] + graph.connections[node][neighbour]
						priority_queue.update_key(__lowercase	,dist[neighbour]					)
						lowerCAmelCase_     :	List[str]							   =					node

    # running prim's algorithm
		while not priority_queue.is_empty():
				lowerCAmelCase_     :	Dict							   =					priority_queue.extract_min()
				for neighbour in graph.connections[node]:
						if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
								lowerCAmelCase_     :	str							   =					dist[node] + graph.connections[node][neighbour]
								priority_queue.update_key(__lowercase	,dist[neighbour]					)
								lowerCAmelCase_     :	Dict							   =					node
		return dist, parent













# DISCLAIMER: This file is strongly influenced by https://github.com/yang-song/score_sde_pytorch

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

import torch

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


@dataclass
class     _a							(	UpperCAmelCase__     ):






  """simple docstring"""





  A_						       = 42
  A_						       = 42




class     _a							(	UpperCAmelCase__    ,							UpperCAmelCase__     ):






  """simple docstring"""





  A_						       = 1




  @register_to_config
  def __init__(  self		,		_UpperCAmelCase = 2000		,		_UpperCAmelCase = 0.1_5		,		_UpperCAmelCase = 0.0_1		,		_UpperCAmelCase = 1_3_4_8.0		,		_UpperCAmelCase = 1e-5		,		_UpperCAmelCase = 1		,		)      ->			Tuple:
     # standard deviation of the initial noise distribution
     UpperCamelCase_						=  sigma_max

     # setable values
     UpperCamelCase_						=  None

     self.set_sigmas(_UpperCAmelCase		,		_UpperCAmelCase		,		_UpperCAmelCase		,		_UpperCAmelCase			)




  def  _UpperCAmelCase  (  self		,		_UpperCAmelCase		,		_UpperCAmelCase = None			)      ->			torch.FloatTensor:
     return sample




  def  _UpperCAmelCase  (  self		,		_UpperCAmelCase		,		_UpperCAmelCase = None		,		_UpperCAmelCase = None			)      ->			str:
     UpperCamelCase_						=  sampling_eps if sampling_eps is not None else self.config.sampling_eps

     UpperCamelCase_						=  torch.linspace(1		,		_UpperCAmelCase		,		_UpperCAmelCase		,		device=_UpperCAmelCase			)




  def  _UpperCAmelCase  (  self		,		_UpperCAmelCase		,		_UpperCAmelCase = None		,		_UpperCAmelCase = None		,		_UpperCAmelCase = None			)      ->			Any:
     UpperCamelCase_						=  sigma_min if sigma_min is not None else self.config.sigma_min
     UpperCamelCase_						=  sigma_max if sigma_max is not None else self.config.sigma_max
     UpperCamelCase_						=  sampling_eps if sampling_eps is not None else self.config.sampling_eps
     if self.timesteps is None:
        self.set_timesteps(_UpperCAmelCase		,		_UpperCAmelCase			)

     UpperCamelCase_						=  sigma_min * (sigma_max / sigma_min) ** (self.timesteps / sampling_eps)
     UpperCamelCase_						=  torch.exp(torch.linspace(math.log(_UpperCAmelCase			)		,		math.log(_UpperCAmelCase			)		,		_UpperCAmelCase			)			)
     UpperCamelCase_						=  torch.tensor([sigma_min * (sigma_max / sigma_min) ** t for t in self.timesteps]			)




  def  _UpperCAmelCase  (  self		,		_UpperCAmelCase		,		_UpperCAmelCase			)      ->			List[Any]:
     return torch.where(
         timesteps == 0		,		torch.zeros_like(t.to(timesteps.device			)			)		,		self.discrete_sigmas[timesteps - 1].to(timesteps.device			)		,		)




  def  _UpperCAmelCase  (  self		,		_UpperCAmelCase		,		_UpperCAmelCase		,		_UpperCAmelCase		,		_UpperCAmelCase = None		,		_UpperCAmelCase = True		,		)      ->			Union[SdeVeOutput, Tuple]:
     if self.timesteps is None:
        raise ValueError(
            '`self.timesteps` is not set, you need to run \'set_timesteps\' after creating the scheduler'			)

     UpperCamelCase_						=  timestep * torch.ones(
         sample.shape[0]		,		device=sample.device			)  # torch.repeat_interleave(timestep, sample.shape[0])
     UpperCamelCase_						=  (timestep * (len(self.timesteps			) - 1)).long()

     # mps requires indices to be in the same device, so we use cpu as is the default with cuda
     UpperCamelCase_						=  timesteps.to(self.discrete_sigmas.device			)

     UpperCamelCase_						=  self.discrete_sigmas[timesteps].to(sample.device			)
     UpperCamelCase_						=  self.get_adjacent_sigma(_UpperCAmelCase		,		_UpperCAmelCase			).to(sample.device			)
     UpperCamelCase_						=  torch.zeros_like(_UpperCAmelCase			)
     UpperCamelCase_						=  (sigma**2 - adjacent_sigma**2) ** 0.5

     # equation 6 in the paper: the model_output modeled by the network is grad_x log pt(x)
     # also equation 47 shows the analog from SDE models to ancestral sampling methods
     UpperCamelCase_						=  diffusion.flatten()
     while len(diffusion.shape			) < len(sample.shape			):
        UpperCamelCase_						=  diffusion.unsqueeze(-1			)
     UpperCamelCase_						=  drift - diffusion**2 * model_output

     #  equation 6: sample noise for the diffusion term of
     UpperCamelCase_						=  randn_tensor(
         sample.shape		,		layout=sample.layout		,		generator=_UpperCAmelCase		,		device=sample.device		,		dtype=sample.dtype			)
     UpperCamelCase_						=  sample - drift  # subtract because `dt` is a small negative timestep
     # TODO is the variable diffusion the correct scaling term for the noise?
     UpperCamelCase_						=  prev_sample_mean + diffusion * noise  # add impact of diffusion field g

     if not return_dict:
        return (prev_sample, prev_sample_mean)

     return SdeVeOutput(prev_sample=_UpperCAmelCase		,		prev_sample_mean=_UpperCAmelCase			)




  def  _UpperCAmelCase  (  self		,		_UpperCAmelCase		,		_UpperCAmelCase		,		_UpperCAmelCase = None		,		_UpperCAmelCase = True		,		)      ->			Union[SchedulerOutput, Tuple]:
     if self.timesteps is None:
        raise ValueError(
            '`self.timesteps` is not set, you need to run \'set_timesteps\' after creating the scheduler'			)

     # For small batch sizes, the paper "suggest replacing norm(z) with sqrt(d), where d is the dim. of z"
     # sample noise for correction
     UpperCamelCase_						=  randn_tensor(sample.shape		,		layout=sample.layout		,		generator=_UpperCAmelCase			).to(sample.device			)

     # compute step size from the model_output, the noise, and the snr
     UpperCamelCase_						=  torch.norm(model_output.reshape(model_output.shape[0]		,		-1			)		,		dim=-1			).mean()
     UpperCamelCase_						=  torch.norm(noise.reshape(noise.shape[0]		,		-1			)		,		dim=-1			).mean()
     UpperCamelCase_						=  (self.config.snr * noise_norm / grad_norm) ** 2 * 2
     UpperCamelCase_						=  step_size * torch.ones(sample.shape[0]			).to(sample.device			)
     # self.repeat_scalar(step_size, sample.shape[0])

     # compute corrected sample: model_output term and noise term
     UpperCamelCase_						=  step_size.flatten()
     while len(step_size.shape			) < len(sample.shape			):
        UpperCamelCase_						=  step_size.unsqueeze(-1			)
     UpperCamelCase_						=  sample + step_size * model_output
     UpperCamelCase_						=  prev_sample_mean + ((step_size * 2) ** 0.5) * noise

     if not return_dict:
        return (prev_sample,)

     return SchedulerOutput(prev_sample=_UpperCAmelCase			)




  def  _UpperCAmelCase  (  self		,		_UpperCAmelCase		,		_UpperCAmelCase		,		_UpperCAmelCase		,		)      ->			torch.FloatTensor:
     # Make sure sigmas and timesteps have the same device and dtype as original_samples
     UpperCamelCase_						=  timesteps.to(original_samples.device			)
     UpperCamelCase_						=  self.discrete_sigmas.to(original_samples.device			)[timesteps]
     UpperCamelCase_						=  (
         noise * sigmas[:, None, None, None]
         if noise is not None
         else torch.randn_like(_UpperCAmelCase			) * sigmas[:, None, None, None]
     )
     UpperCamelCase_						=  noise + original_samples
     return noisy_samples




  def __len__(  self			)      ->			Optional[int]:
     return self.config.num_train_timesteps





