


"""simple docstring"""







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

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils import SchedulerMixin, SchedulerOutput




class 			UpperCamelCase_     (			UpperCamelCase      ,  UpperCamelCase):

	"""simple docstring"""





	snake_case__    :  List[Any]    =      1




	@register_to_config
	def __init__(			self      :    Dict      ,      UpperCAmelCase__      :    int = 1_0_0_0      ,      UpperCAmelCase__      :    Optional[Union[np.ndarray, List[float]]] = None       )	->     Optional[int]:
						# set `betas`, `alphas`, `timesteps`
						self.set_timesteps(UpperCAmelCase__       )

						# standard deviation of the initial noise distribution
						__SCREAMING_SNAKE_CASE						       =    1.0

						# For now we only support F-PNDM, i.e. the runge-kutta method
						# For more information on the algorithm please take a look at the paper: https://arxiv.org/pdf/2202.09778.pdf
						# mainly at formula (9), (12), (13) and the Algorithm 2.
						__SCREAMING_SNAKE_CASE						       =    4

						# running values
						__SCREAMING_SNAKE_CASE						       =    []




	def   UpperCAmelCase_				(			self      :    Tuple      ,      UpperCAmelCase__      :    int      ,      UpperCAmelCase__      :    Union[str, torch.device] = None       )	->     str:
						__SCREAMING_SNAKE_CASE						       =    num_inference_steps
						__SCREAMING_SNAKE_CASE						       =    torch.linspace(1      ,      0      ,      num_inference_steps + 1       )[:-1]
						__SCREAMING_SNAKE_CASE						       =    torch.cat([steps, torch.tensor([0.0]       )]       )

						if self.config.trained_betas is not None:
											__SCREAMING_SNAKE_CASE						       =    torch.tensor(self.config.trained_betas      ,      dtype=torch.floataa       )
						else:
											__SCREAMING_SNAKE_CASE						       =    torch.sin(steps * math.pi / 2       ) ** 2

						__SCREAMING_SNAKE_CASE						       =    (1.0 - self.betas**2) ** 0.5

						__SCREAMING_SNAKE_CASE						       =    (torch.atana(self.betas      ,      self.alphas       ) / math.pi * 2)[:-1]
						__SCREAMING_SNAKE_CASE						       =    timesteps.to(UpperCAmelCase__       )

						__SCREAMING_SNAKE_CASE						       =    []




	def   UpperCAmelCase_				(			self      :    List[str]      ,      UpperCAmelCase__      :    torch.FloatTensor      ,      UpperCAmelCase__      :    int      ,      UpperCAmelCase__      :    torch.FloatTensor      ,      UpperCAmelCase__      :    bool = True      ,      )	->     Union[SchedulerOutput, Tuple]:
						if self.num_inference_steps is None:
											raise ValueError(
											    "Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"       )

						__SCREAMING_SNAKE_CASE						       =    (self.timesteps == timestep).nonzero().item()
						__SCREAMING_SNAKE_CASE						       =    timestep_index + 1

						__SCREAMING_SNAKE_CASE						       =    sample * self.betas[timestep_index] + model_output * self.alphas[timestep_index]
						self.ets.append(UpperCAmelCase__       )

						if len(self.ets       ) == 1:
											__SCREAMING_SNAKE_CASE						       =    self.ets[-1]
						elif len(self.ets       ) == 2:
											__SCREAMING_SNAKE_CASE						       =    (3 * self.ets[-1] - self.ets[-2]) / 2
						elif len(self.ets       ) == 3:
											__SCREAMING_SNAKE_CASE						       =    (2_3 * self.ets[-1] - 1_6 * self.ets[-2] + 5 * self.ets[-3]) / 1_2
						else:
											__SCREAMING_SNAKE_CASE						       =    (1 / 2_4) * (5_5 * self.ets[-1] - 5_9 * self.ets[-2] + 3_7 * self.ets[-3] - 9 * self.ets[-4])

						__SCREAMING_SNAKE_CASE						       =    self._get_prev_sample(UpperCAmelCase__      ,      UpperCAmelCase__      ,      UpperCAmelCase__      ,      UpperCAmelCase__       )

						if not return_dict:
											return (prev_sample,)

						return SchedulerOutput(prev_sample=UpperCAmelCase__       )




	def   UpperCAmelCase_				(			self      :    Dict      ,      UpperCAmelCase__      :    torch.FloatTensor      ,      *UpperCAmelCase__      :    Optional[Any]      ,      **UpperCAmelCase__      :    int       )	->     torch.FloatTensor:
						return sample




	def   UpperCAmelCase_				(			self      :    Optional[int]      ,      UpperCAmelCase__      :    Optional[Any]      ,      UpperCAmelCase__      :    Union[str, Any]      ,      UpperCAmelCase__      :    str      ,      UpperCAmelCase__      :    int       )	->     Any:
						__SCREAMING_SNAKE_CASE						       =    self.alphas[timestep_index]
						__SCREAMING_SNAKE_CASE						       =    self.betas[timestep_index]

						__SCREAMING_SNAKE_CASE						       =    self.alphas[prev_timestep_index]
						__SCREAMING_SNAKE_CASE						       =    self.betas[prev_timestep_index]

						__SCREAMING_SNAKE_CASE						       =    (sample - sigma * ets) / max(UpperCAmelCase__      ,      1E-8       )
						__SCREAMING_SNAKE_CASE						       =    next_alpha * pred + ets * next_sigma

						return prev_sample




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




"""simple docstring"""







from __future__ import annotations




def        UpperCAmelCase__	(lowerCAmelCase_  ,						lowerCAmelCase_       ):




					'''simple docstring'''


					print(f"""Vertex\tShortest Distance from vertex {src}"""       )
					for i, d in enumerate(lowerCAmelCase_       ):
										print(f"""{i}\t\t{d}"""       )




def        UpperCAmelCase__	(lowerCAmelCase_  ,						lowerCAmelCase_  ,						lowerCAmelCase_       ):




					'''simple docstring'''


					for j in range(lowerCAmelCase_       ):
										__SCREAMING_SNAKE_CASE       ,  __SCREAMING_SNAKE_CASE       ,  __SCREAMING_SNAKE_CASE						       =    (graph[j][k] for k in ["src", "dst", "weight"])
										if distance[u] != float("inf"       ) and distance[u] + w < distance[v]:
															return True
					return False




def        UpperCAmelCase__	(lowerCAmelCase_  ,						lowerCAmelCase_  ,						lowerCAmelCase_  ,						lowerCAmelCase_       ):




					'''simple docstring'''


					__SCREAMING_SNAKE_CASE						       =    [float("inf"       )] * vertex_count
					__SCREAMING_SNAKE_CASE						       =    0.0

					for _ in range(vertex_count - 1       ):
										for j in range(lowerCAmelCase_       ):
															__SCREAMING_SNAKE_CASE       ,  __SCREAMING_SNAKE_CASE       ,  __SCREAMING_SNAKE_CASE						       =    (graph[j][k] for k in ["src", "dst", "weight"])

															if distance[u] != float("inf"       ) and distance[u] + w < distance[v]:
																				__SCREAMING_SNAKE_CASE						       =    distance[u] + w

					__SCREAMING_SNAKE_CASE						       =    check_negative_cycle(lowerCAmelCase_  ,						lowerCAmelCase_  ,						lowerCAmelCase_       )
					if negative_cycle_exists:
										raise Exception("Negative cycle found"       )

					return distance


if __name__ == "__main__":
		import doctest

		doctest.testmod()

		a__    :							Union[str, Any]            =					int(input('''Enter number of vertices: ''').strip())
		a__    :							Any            =					int(input('''Enter number of edges: ''').strip())

		a__    :							list[dict[str, int]]            =					[{} for _ in range(E)]

		for i in range(E):
				print('''Edge ''', i + 1)
				a__      ,					a__      ,					a__    :							str            =					(
				    int(x)
				    for x in input('''Enter source, destination, weight: ''').strip().split(''' ''')
				)
				a__    :							str            =					{'''src''': src, '''dst''': dest, '''weight''': weight}

		a__    :							str            =					int(input('''\nEnter shortest path source:''').strip())
		a__    :							List[Any]            =					bellman_ford(graph, V, E, source)
		print_distance(shortest_distance, 0)
