





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_						(					_lowerCamelCase							,					_lowerCamelCase   ):
					lowerCAmelCase_							=		1




					@register_to_config
					def __init__(						self			,  lowerCAmelCase_ = 1000			,  lowerCAmelCase_ = None					)						->							Optional[int]:
										# set `betas`, `alphas`, `timesteps`
										self.set_timesteps(lowerCAmelCase_					)

										# standard deviation of the initial noise distribution
										_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.
										_snake_case													=			4

										# running values
										_snake_case													=			[]




					def 		lowerCAmelCase     (						self			,  lowerCAmelCase_			,  lowerCAmelCase_ = None					)						->							List[str]:
										_snake_case													=			num_inference_steps
										_snake_case													=			torch.linspace(1			,  0			,  num_inference_steps + 1					)[:-1]
										_snake_case													=			torch.cat([steps, torch.tensor([0.0]					)]					)

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

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

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

										_snake_case													=			[]




					def 		lowerCAmelCase     (						self			,  lowerCAmelCase_			,  lowerCAmelCase_			,  lowerCAmelCase_			,  lowerCAmelCase_ = 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'					)

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

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

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

										_snake_case													=			self._get_prev_sample(lowerCAmelCase_			,  lowerCAmelCase_			,  lowerCAmelCase_			,  lowerCAmelCase_					)

										if not return_dict:
															return (prev_sample,)

										return SchedulerOutput(prev_sample=lowerCAmelCase_					)




					def 		lowerCAmelCase     (						self			,  lowerCAmelCase_			,  *lowerCAmelCase_			,  **lowerCAmelCase_					)						->							torch.FloatTensor:
										return sample




					def 		lowerCAmelCase     (						self			,  lowerCAmelCase_			,  lowerCAmelCase_			,  lowerCAmelCase_			,  lowerCAmelCase_					)						->							Any:
										_snake_case													=			self.alphas[timestep_index]
										_snake_case													=			self.betas[timestep_index]

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

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

										return prev_sample






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










def   lowerCamelCase__       (       UpperCamelCase__     :    Tuple    ,      UpperCamelCase__     :    Optional[int]  )     ->	Tuple:



					'''simple docstring'''




					_snake_case													=			[0 for i in range(r + 1  )]
					# nc0 = 1
					_snake_case													=			1
					for i in range(1    ,      n + 1  ):
										# to compute current row from previous row.
										_snake_case													=			min(UpperCamelCase__    ,      UpperCamelCase__  )
										while j > 0:
															c[j] += c[j - 1]
															j -= 1
					return c[r]




print(binomial_coefficient(n=10, r=5))



