

'''simple docstring'''

import math
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 KarrasDiffusionSchedulers, SchedulerMixin


lowerCAmelCase_     =      logging.get_logger(__name__)  # pylint: disable=invalid-name







@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerAncestralDiscrete
class lowerCamelCase   (    __lowerCAmelCase				):
				snake_case_							     = 42
				snake_case_							     = None

def      __magic_name__							(			A       , A=0.999       , A="cosine"       , )      ->		Optional[int]:
	if alpha_transform_type == "cosine":

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

	elif alpha_transform_type == "exp":

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

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

	snake_case							=					[]
	for i in range(A				):
		snake_case							=					i / num_diffusion_timesteps
		snake_case							=					(i + 1) / num_diffusion_timesteps
		betas.append(min(1 - alpha_bar_fn(A				) / alpha_bar_fn(A				)       , A				)				)
	return torch.tensor(A       , dtype=torch.floataa				)







class lowerCamelCase   (    __lowerCAmelCase				,				__lowerCAmelCase				):
				snake_case_							     = [e.name for e in KarrasDiffusionSchedulers]
				snake_case_							     = 1

				@register_to_config
				def __init__(       self,						lowercase_ = 1000,						lowercase_ = 0.0_001,						lowercase_ = 0.02,						lowercase_ = "linear",						lowercase_ = None,						lowercase_ = "epsilon",						lowercase_ = "linspace",						lowercase_ = 0,						)    ->							List[str]:
					if trained_betas is not None:
						snake_case							=					torch.tensor(lowercase_,						dtype=torch.floataa )
					elif beta_schedule == "linear":
						snake_case							=					torch.linspace(lowercase_,						lowercase_,						lowercase_,						dtype=torch.floataa )
					elif beta_schedule == "scaled_linear":
						# this schedule is very specific to the latent diffusion model.
						snake_case							=					(
						    torch.linspace(beta_start**0.5,						beta_end**0.5,						lowercase_,						dtype=torch.floataa ) ** 2
						)
					elif beta_schedule == "squaredcos_cap_v2":
						# Glide cosine schedule
						snake_case							=					betas_for_alpha_bar(lowercase_ )
					else:
						raise NotImplementedError(F'''{beta_schedule} does is not implemented for {self.__class__}''' )

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

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

					# setable values
					snake_case							=					None
					snake_case							=					np.linspace(0,						num_train_timesteps - 1,						lowercase_,						dtype=lowercase_ )[::-1].copy()
					snake_case							=					torch.from_numpy(lowercase_ )
					snake_case							=					False

				@property
				def 					_lowerCamelCase    (       self )    ->							Any:
					# standard deviation of the initial noise distribution
					if self.config.timestep_spacing in ["linspace", "trailing"]:
						return self.sigmas.max()

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

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

				def 					_lowerCamelCase    (       self,						lowercase_,						lowercase_ = None )    ->							List[Any]:
					snake_case							=					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":
						snake_case							=					np.linspace(0,						self.config.num_train_timesteps - 1,						lowercase_,						dtype=lowercase_ )[
						    ::-1
						].copy()
					elif self.config.timestep_spacing == "leading":
						snake_case							=					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
						snake_case							=					(np.arange(0,						lowercase_ ) * step_ratio).round()[::-1].copy().astype(lowercase_ )
						timesteps += self.config.steps_offset
					elif self.config.timestep_spacing == "trailing":
						snake_case							=					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
						snake_case							=					(np.arange(self.config.num_train_timesteps,						0,						-step_ratio )).round().copy().astype(lowercase_ )
						timesteps -= 1
					else:
						raise ValueError(
						    F'''{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.''' )

					snake_case							=					np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5 )
					snake_case							=					np.interp(lowercase_,						np.arange(0,						len(lowercase_ ) ),						lowercase_ )
					snake_case							=					np.concatenate([sigmas, [0.0]] ).astype(np.floataa )
					snake_case							=					torch.from_numpy(lowercase_ ).to(device=lowercase_ )
					if str(lowercase_ ).startswith('mps' ):
						# mps does not support float64
						snake_case							=					torch.from_numpy(lowercase_ ).to(lowercase_,						dtype=torch.floataa )
					else:
						snake_case							=					torch.from_numpy(lowercase_ ).to(device=lowercase_ )

				def 					_lowerCamelCase    (       self,						lowercase_,						lowercase_,						lowercase_,						lowercase_ = None,						lowercase_ = True,						)    ->							Union[EulerAncestralDiscreteSchedulerOutput, Tuple]:

					if (
					    isinstance(lowercase_,						lowercase_ )
					    or isinstance(lowercase_,						torch.IntTensor )
					    or isinstance(lowercase_,						torch.LongTensor )
					):
						raise ValueError(
						    (
						        'Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to'
						        ' `EulerDiscreteScheduler.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(lowercase_,						torch.Tensor ):
						snake_case							=					timestep.to(self.timesteps.device )

					snake_case							=					(self.timesteps == timestep).nonzero().item()
					snake_case							=					self.sigmas[step_index]

					# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
					if self.config.prediction_type == "epsilon":
						snake_case							=					sample - sigma * model_output
					elif self.config.prediction_type == "v_prediction":
						# * c_out + input * c_skip
						snake_case							=					model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**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`''' )

					snake_case							=					self.sigmas[step_index]
					snake_case							=					self.sigmas[step_index + 1]
					snake_case							=					(sigma_to**2 * (sigma_from**2 - sigma_to**2) / sigma_from**2) ** 0.5
					snake_case							=					(sigma_to**2 - sigma_up**2) ** 0.5

					# 2. Convert to an ODE derivative
					snake_case							=					(sample - pred_original_sample) / sigma

					snake_case							=					sigma_down - sigma

					snake_case							=					sample + derivative * dt

					snake_case							=					model_output.device
					snake_case							=					randn_tensor(model_output.shape,						dtype=model_output.dtype,						device=lowercase_,						generator=lowercase_ )

					snake_case							=					prev_sample + noise * sigma_up

					if not return_dict:
						return (prev_sample,)

					return EulerAncestralDiscreteSchedulerOutput(
					    prev_sample=lowercase_,						pred_original_sample=lowercase_ )

				def 					_lowerCamelCase    (       self,						lowercase_,						lowercase_,						lowercase_,						)    ->							torch.FloatTensor:
					# Make sure sigmas and timesteps have the same device and dtype as original_samples
					snake_case							=					self.sigmas.to(device=original_samples.device,						dtype=original_samples.dtype )
					if original_samples.device.type == "mps" and torch.is_floating_point(lowercase_ ):
						# mps does not support float64
						snake_case							=					self.timesteps.to(original_samples.device,						dtype=torch.floataa )
						snake_case							=					timesteps.to(original_samples.device,						dtype=torch.floataa )
					else:
						snake_case							=					self.timesteps.to(original_samples.device )
						snake_case							=					timesteps.to(original_samples.device )

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

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

					snake_case							=					original_samples + noise * sigma
					return noisy_samples






				def __len__(       self )    ->							List[str]:
					return self.config.num_train_timesteps













import math
import sys



class  __UpperCAmelCase						:







			def __init__(      self:    str	):







									'''simple docstring'''




									_SCREAMING_SNAKE_CASE       =    0
									_SCREAMING_SNAKE_CASE       =    []
									_SCREAMING_SNAKE_CASE       =    {}  # To store the pos of node in array







			def 				UpperCamelCase (      self:    List[str]	):







									'''simple docstring'''




									return self.cur_size == 0







			def 				UpperCamelCase (      self:    int ,      UpperCAmelCase_:    Union[str, Any]	):







									'''simple docstring'''




									_SCREAMING_SNAKE_CASE       =    self.left(UpperCAmelCase_	)
									_SCREAMING_SNAKE_CASE       =    self.right(UpperCAmelCase_	)
									if lc < self.cur_size and self.array(UpperCAmelCase_	)[0] < self.array(UpperCAmelCase_	)[0]:
															_SCREAMING_SNAKE_CASE       =    lc
									else:
															_SCREAMING_SNAKE_CASE       =    idx
									if rc < self.cur_size and self.array(UpperCAmelCase_	)[0] < self.array(UpperCAmelCase_	)[0]:
															_SCREAMING_SNAKE_CASE       =    rc
									if smallest != idx:
															self.swap(UpperCAmelCase_ ,      UpperCAmelCase_	)
															self.min_heapify(UpperCAmelCase_	)







			def 				UpperCamelCase (      self:    int ,      UpperCAmelCase_:    Tuple	):







									'''simple docstring'''




									_SCREAMING_SNAKE_CASE       =    self.cur_size
									self.cur_size += 1
									self.array.append((sys.maxsize, tup[1])	)
									self.decrease_key((sys.maxsize, tup[1]) ,      tup[0]	)







			def 				UpperCamelCase (      self:    Union[str, Any]	):







									'''simple docstring'''




									_SCREAMING_SNAKE_CASE       =    self.array[0][1]
									_SCREAMING_SNAKE_CASE       =    self.array[self.cur_size - 1]
									self.cur_size -= 1
									self.min_heapify(1	)
									del self.pos[min_node]
									return min_node







			def 				UpperCamelCase (      self:    Dict ,      UpperCAmelCase_:    List[Any]	):







									'''simple docstring'''




									return 2 * i + 1







			def 				UpperCamelCase (      self:    Optional[Any] ,      UpperCAmelCase_:    List[Any]	):







									'''simple docstring'''




									return 2 * i + 2







			def 				UpperCamelCase (      self:    Union[str, Any] ,      UpperCAmelCase_:    int	):







									'''simple docstring'''




									return math.floor(i / 2	)







			def 				UpperCamelCase (      self:    str ,      UpperCAmelCase_:    Optional[Any] ,      UpperCAmelCase_:    str	):







									'''simple docstring'''




									_SCREAMING_SNAKE_CASE       =    j
									_SCREAMING_SNAKE_CASE       =    i
									_SCREAMING_SNAKE_CASE       =    self.array[i]
									_SCREAMING_SNAKE_CASE       =    self.array[j]
									_SCREAMING_SNAKE_CASE       =    temp







			def 				UpperCamelCase (      self:    int ,      UpperCAmelCase_:    Dict ,      UpperCAmelCase_:    Dict	):







									'''simple docstring'''




									_SCREAMING_SNAKE_CASE       =    self.pos[tup[1]]
									# assuming the new_d is atmost old_d
									_SCREAMING_SNAKE_CASE       =    (new_d, tup[1])
									while idx > 0 and self.array[self.par(UpperCAmelCase_	)][0] > self.array[idx][0]:
															self.swap(UpperCAmelCase_ ,      self.par(UpperCAmelCase_	)	)
															_SCREAMING_SNAKE_CASE       =    self.par(UpperCAmelCase_	)



class  __UpperCAmelCase						:







			def __init__(      self:    Tuple ,      UpperCAmelCase_:    Any	):







									'''simple docstring'''




									_SCREAMING_SNAKE_CASE       =    {}  # To store graph: u -> (v,w)
									_SCREAMING_SNAKE_CASE       =    num  # Number of nodes in graph
									# To store the distance from source vertex
									_SCREAMING_SNAKE_CASE       =    [0] * self.num_nodes
									_SCREAMING_SNAKE_CASE       =    [-1] * self.num_nodes  # To store the path







			def 				UpperCamelCase (      self:    Tuple ,      UpperCAmelCase_:    int ,      UpperCAmelCase_:    List[Any] ,      UpperCAmelCase_:    Any	):







									'''simple docstring'''




									if u in self.adjList:
															self.adjList[u].append((v, w)	)
									else:
															_SCREAMING_SNAKE_CASE       =    [(v, w)]

									# Assuming undirected graph
									if v in self.adjList:
															self.adjList[v].append((u, w)	)
									else:
															_SCREAMING_SNAKE_CASE       =    [(u, w)]







			def 				UpperCamelCase (      self:    Dict	):







									'''simple docstring'''




									for u in self.adjList:
															print(UpperCAmelCase_ ,      """->""" ,      """ -> """.join(str(F'{v}({w})'	) for v, w in self.adjList[u]	)	)







			def 				UpperCamelCase (      self:    Optional[int] ,      UpperCAmelCase_:    str	):







									'''simple docstring'''




									_SCREAMING_SNAKE_CASE       =    [-1] * self.num_nodes
									# src is the source node
									_SCREAMING_SNAKE_CASE       =    0
									_SCREAMING_SNAKE_CASE       =    PriorityQueue()
									q.insert((0, src)	)  # (dist from src, node)
									for u in self.adjList:
															if u != src:
																					_SCREAMING_SNAKE_CASE       =    sys.maxsize  # Infinity
																					_SCREAMING_SNAKE_CASE       =    -1

									while not q.is_empty():
															_SCREAMING_SNAKE_CASE       =    q.extract_min()  # Returns node with the min dist from source
															# Update the distance of all the neighbours of u and
															# if their prev dist was INFINITY then push them in Q
															for v, w in self.adjList[u]:
																					_SCREAMING_SNAKE_CASE       =    self.dist[u] + w
																					if self.dist[v] > new_dist:
																											if self.dist[v] == sys.maxsize:
																																	q.insert((new_dist, v)	)
																											else:
																																	q.decrease_key((self.dist[v], v) ,      UpperCAmelCase_	)
																											_SCREAMING_SNAKE_CASE       =    new_dist
																											_SCREAMING_SNAKE_CASE       =    u

        # Show the shortest distances from src
									self.show_distances(UpperCAmelCase_	)







			def 				UpperCamelCase (      self:    Optional[int] ,      UpperCAmelCase_:    int	):







									'''simple docstring'''




									print(F'Distance from node: {src}'	)
									for u in range(self.num_nodes	):
															print(F'Node {u} has distance: {self.dist[u]}'	)







			def 				UpperCamelCase (      self:    str ,      UpperCAmelCase_:    str ,      UpperCAmelCase_:    List[str]	):







									'''simple docstring'''




									_SCREAMING_SNAKE_CASE       =    []
									_SCREAMING_SNAKE_CASE       =    0
									_SCREAMING_SNAKE_CASE       =    dest
									# Backtracking from dest to src
									while self.par[temp] != -1:
															path.append(UpperCAmelCase_	)
															if temp != src:
																					for v, w in self.adjList[temp]:
																											if v == self.par[temp]:
																																	cost += w
																																	break
															_SCREAMING_SNAKE_CASE       =    self.par[temp]
									path.append(UpperCAmelCase_	)
									path.reverse()

									print(F'----Path to reach {dest} from {src}----'	)
									for u in path:
															print(F'{u}' ,      end=""" """	)
															if u != dest:
																					print("""-> """ ,      end=""""""	)

									print("""\nTotal cost of path: """ ,      UpperCAmelCase_	)


if __name__ == "__main__":
		UpperCamelCase												=      Graph(9)
		graph.add_edge(0, 1, 4)
		graph.add_edge(0, 7, 8)
		graph.add_edge(1, 2, 8)
		graph.add_edge(1, 7, 11)
		graph.add_edge(2, 3, 7)
		graph.add_edge(2, 8, 2)
		graph.add_edge(2, 5, 4)
		graph.add_edge(3, 4, 9)
		graph.add_edge(3, 5, 14)
		graph.add_edge(4, 5, 10)
		graph.add_edge(5, 6, 2)
		graph.add_edge(6, 7, 1)
		graph.add_edge(6, 8, 6)
		graph.add_edge(7, 8, 7)
		graph.show_graph()
		graph.dijkstra(0)
		graph.show_path(0, 4)

# OUTPUT
# 0 -> 1(4) -> 7(8)
# 1 -> 0(4) -> 2(8) -> 7(11)
# 7 -> 0(8) -> 1(11) -> 6(1) -> 8(7)
# 2 -> 1(8) -> 3(7) -> 8(2) -> 5(4)
# 3 -> 2(7) -> 4(9) -> 5(14)
# 8 -> 2(2) -> 6(6) -> 7(7)
# 5 -> 2(4) -> 3(14) -> 4(10) -> 6(2)
# 4 -> 3(9) -> 5(10)
# 6 -> 5(2) -> 7(1) -> 8(6)
# Distance from node: 0
# Node 0 has distance: 0
# Node 1 has distance: 4
# Node 2 has distance: 12
# Node 3 has distance: 19
# Node 4 has distance: 21
# Node 5 has distance: 11
# Node 6 has distance: 9
# Node 7 has distance: 8
# Node 8 has distance: 14
# ----Path to reach 4 from 0----
# 0 -> 7 -> 6 -> 5 -> 4
# Total cost of path:  21

