



'''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      _lowerCAmelCase							(      __UpperCAmelCase				,      __UpperCAmelCase			):
	__SCREAMING_SNAKE_CASE       :		int		      = 1


	@register_to_config
	def __init__(self	,				lowercase = 1000	,				lowercase = None							):
				# set `betas`, `alphas`, `timesteps`
				self.set_timesteps(lowercase							)

				# standard deviation of the initial noise distribution
				A_     :						List[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.
				A_     :						Optional[int]     =					4

				# running values
				A_     :						int     =					[]


	def    _a     (self	,				lowercase	,				lowercase = None							):
				A_     :						Dict     =					num_inference_steps
				A_     :						Optional[Any]     =					torch.linspace(1	,				0	,				num_inference_steps + 1							)[:-1]
				A_     :						Optional[Any]     =					torch.cat([steps, torch.tensor([0.0]							)]							)

				if self.config.trained_betas is not None:
							A_     :						Optional[int]     =					torch.tensor(self.config.trained_betas	,				dtype=torch.floataa							)
				else:
							A_     :						Dict     =					torch.sin(steps * math.pi / 2							) ** 2

				A_     :						int     =					(1.0 - self.betas**2) ** 0.5

				A_     :						Optional[Any]     =					(torch.atana(self.betas	,				self.alphas							) / math.pi * 2)[:-1]
				A_     :						Dict     =					timesteps.to(lowercase							)

				A_     :						Dict     =					[]


	def    _a     (self	,				lowercase	,				lowercase	,				lowercase	,				lowercase = True	,				):
				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"""							)

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

				A_     :						Dict     =					sample * self.betas[timestep_index] + model_output * self.alphas[timestep_index]
				self.ets.append(lowercase							)

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

				A_     :						List[Any]     =					self._get_prev_sample(lowercase	,				lowercase	,				lowercase	,				lowercase							)

				if not return_dict:
							return (prev_sample,)

				return SchedulerOutput(prev_sample=lowercase							)


	def    _a     (self	,				lowercase	,				*lowercase	,				**lowercase							):
				return sample


	def    _a     (self	,				lowercase	,				lowercase	,				lowercase	,				lowercase							):
				A_     :						List[Any]     =					self.alphas[timestep_index]
				A_     :						Union[str, Any]     =					self.betas[timestep_index]

				A_     :						int     =					self.alphas[prev_timestep_index]
				A_     :						Optional[Any]     =					self.betas[prev_timestep_index]

				A_     :						List[Any]     =					(sample - sigma * ets) / max(lowercase	,				1E-8							)
				A_     :						Union[str, Any]     =					next_alpha * pred + ets * next_sigma

				return prev_sample


	def __len__(self							):
				return self.config.num_train_timesteps




'''simple docstring'''




def      a      (			):
			'''simple docstring'''





			A_     :						Optional[int]     =					[31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]

			A_     :						Dict     =					6
			A_     :						List[Any]     =					1
			A_     :						Optional[Any]     =					19_01

			A_     :						Tuple     =					0

			while year < 20_01:
						day += 7

						if (year % 4 == 0 and year % 1_00 != 0) or (year % 4_00 == 0):
									if day > days_per_month[month - 1] and month != 2:
												month += 1
												A_     :						Optional[Any]     =					day - days_per_month[month - 2]
									elif day > 29 and month == 2:
												month += 1
												A_     :						str     =					day - 29
						else:
									if day > days_per_month[month - 1]:
												month += 1
												A_     :						List[str]     =					day - days_per_month[month - 2]

						if month > 12:
									year += 1
									A_     :						Tuple     =					1

						if year < 20_01 and day == 1:
									sundays += 1
			return sundays


if __name__ == "__main__":
						print(solution())