

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							(							snake_case__							,		snake_case__      ):
			'''simple docstring'''







			lowerCamelCase__							=1
			@register_to_config
			def __init__(	self							:       Optional[int]					,					a							:       Dict = 1000					,					a							:       List[Any] = None		)							->				Any:

				"""simple docstring"""

				self.set_timesteps(_A		)

				# standard deviation of the initial noise distribution
				SCREAMING_SNAKE_CASE      :					Optional[Any]    =				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      :					List[Any]    =				4

				# running values
				SCREAMING_SNAKE_CASE      :					Union[str, Any]    =				[]
			def 							__UpperCamelCase       (	self							:       Optional[Any]					,					a							:       Tuple					,					a							:       int = None		)							->				Union[str, Any]:

				"""simple docstring"""

				SCREAMING_SNAKE_CASE      :					Union[str, Any]    =				num_inference_steps
				SCREAMING_SNAKE_CASE      :					str    =				torch.linspace(1					,					0					,					num_inference_steps + 1		)[:-1]
				SCREAMING_SNAKE_CASE      :					Optional[Any]    =				torch.cat([steps, torch.tensor([0.0]		)]		)

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

				SCREAMING_SNAKE_CASE      :					Union[str, Any]    =				(1.0 - self.betas**2) ** 0.5

				SCREAMING_SNAKE_CASE      :					Union[str, Any]    =				(torch.atana(self.betas					,					self.alphas		) / math.pi * 2)[:-1]
				SCREAMING_SNAKE_CASE      :					Tuple    =				timesteps.to(_A		)

				SCREAMING_SNAKE_CASE      :					Optional[Any]    =				[]
			def 							__UpperCamelCase       (	self							:       List[Any]					,					a							:       int					,					a							:       Optional[Any]					,					a							:       Optional[Any]					,					a							:       Any = True					,					)							->				str:

				"""simple docstring"""

				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      :					List[Any]    =				(self.timesteps == timestep).nonzero().item()
				SCREAMING_SNAKE_CASE      :					Tuple    =				timestep_index + 1

				SCREAMING_SNAKE_CASE      :					Union[str, Any]    =				sample * self.betas[timestep_index] + model_output * self.alphas[timestep_index]
				self.ets.append(_A		)

				if len(self.ets		) == 1:
					SCREAMING_SNAKE_CASE      :					Optional[Any]    =				self.ets[-1]
				elif len(self.ets		) == 2:
					SCREAMING_SNAKE_CASE      :					Optional[int]    =				(3 * self.ets[-1] - self.ets[-2]) / 2
				elif len(self.ets		) == 3:
					SCREAMING_SNAKE_CASE      :					Any    =				(23 * self.ets[-1] - 16 * self.ets[-2] + 5 * self.ets[-3]) / 12
				else:
					SCREAMING_SNAKE_CASE      :					Any    =				(1 / 24) * (55 * self.ets[-1] - 59 * self.ets[-2] + 37 * self.ets[-3] - 9 * self.ets[-4])

				SCREAMING_SNAKE_CASE      :					Tuple    =				self._get_prev_sample(_A					,					_A					,					_A					,					_A		)

				if not return_dict:
					return (prev_sample,)

				return SchedulerOutput(prev_sample=_A		)
			def 							__UpperCamelCase       (	self							:       Optional[int]					,					a							:       Dict					,					*a							:       Union[str, Any]					,					**a							:       Tuple		)							->				Optional[int]:

				"""simple docstring"""

				return sample
			def 							__UpperCamelCase       (	self							:       Union[str, Any]					,					a							:       List[str]					,					a							:       Union[str, Any]					,					a							:       Tuple					,					a							:       Optional[Any]		)							->				List[str]:

				"""simple docstring"""

				SCREAMING_SNAKE_CASE      :					Optional[int]    =				self.alphas[timestep_index]
				SCREAMING_SNAKE_CASE      :					Dict    =				self.betas[timestep_index]

				SCREAMING_SNAKE_CASE      :					List[Any]    =				self.alphas[prev_timestep_index]
				SCREAMING_SNAKE_CASE      :					str    =				self.betas[prev_timestep_index]

				SCREAMING_SNAKE_CASE      :					List[Any]    =				(sample - sigma * ets) / max(_A					,					1e-8		)
				SCREAMING_SNAKE_CASE      :					str    =				next_alpha * pred + ets * next_sigma

				return prev_sample






			def __len__(	self							:       Any		)							->				Tuple:

				"""simple docstring"""

				return self.config.num_train_timesteps






def  _SCREAMING_SNAKE_CASE				(   a					,						a  )      ->      list[int]:
					__A	:						Optional[int]       =				int(a  )

					# Initialize Result
					__A	:						Optional[int]       =				[]

					# Traverse through all denomination
					for denomination in reversed(a  ):
										# Find denominations
										while int(a  ) >= int(a  ):
															total_value -= int(a  )
															answer.append(a  )  # Append the "answers" array

					return answer


# Driver Code
if __name__ == "__main__":
				UpperCAmelCase						:   List[str]			  =     []
				UpperCAmelCase						:   Optional[int]			  =     '''0'''

				if (
				    input('''Do you want to enter your denominations ? (yY/n): ''').strip().lower()
				    == "y"
				):
								UpperCAmelCase						:   List[Any]			  =     int(input('''Enter the number of denominations you want to add: ''').strip())

								for i in range(0, n):
												denominations.append(int(input(F"""Denomination {i}: """).strip()))
								UpperCAmelCase						:   int			  =     input('''Enter the change you want to make in Indian Currency: ''').strip()
				else:
								# All denominations of Indian Currency if user does not enter
								UpperCAmelCase						:   Optional[int]			  =     [1, 2, 5, 10, 20, 50, 1_00, 5_00, 20_00]
								UpperCAmelCase						:   Tuple			  =     input('''Enter the change you want to make: ''').strip()

				if int(value) == 0 or int(value) < 0:
								print('''The total value cannot be zero or negative.''')

				else:
								print(F"""Following is minimal change for {value}: """)
								UpperCAmelCase						:   Optional[int]			  =     find_minimum_change(denominations, value)
								# Print result
								for i in range(len(answer)):
												print(answer[i], end=''' ''')




