
import math
from typing import Union

import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import randn_tensor
from .scheduling_utils import SchedulerMixin

class __snake_case						( lowerCAmelCase   ,      lowerCAmelCase	):
    _a						:		Optional[Any]=							1
    @register_to_config
    def __init__(    self						,snake_case=2000						,snake_case=0.1						,snake_case=20						,snake_case=1e-3 ):



           '''simple docstring'''







           lowercase				:	Union[str, Any]			      = None
           lowercase				:	Union[str, Any]			      = None
           lowercase				:	int			      = None
    def  _SCREAMING_SNAKE_CASE			(    self						,snake_case						,snake_case = None ):



           '''simple docstring'''







           lowercase				:	int			      = torch.linspace(1						,self.config.sampling_eps						,lowerCamelCase__						,device=lowerCamelCase__ )
    def  _SCREAMING_SNAKE_CASE			(    self						,snake_case						,snake_case						,snake_case						,snake_case=None ):



           '''simple docstring'''







           if self.timesteps is None:
                  raise ValueError(
                      """`self.timesteps` is not set, you need to run \'set_timesteps\' after creating the scheduler""" )

           # TODO(Patrick) better comments + non-PyTorch
           # postprocess model score
           lowercase				:	Union[str, Any]			      = (
               -0.25 * t**2 * (self.config.beta_max - self.config.beta_min) - 0.5 * t * self.config.beta_min
           )
           lowercase				:	str			      = torch.sqrt(1.0 - torch.exp(2.0 * log_mean_coeff ) )
           lowercase				:	Dict			      = std.flatten()
           while len(std.shape ) < len(score.shape ):
                  lowercase				:	List[Any]			      = std.unsqueeze(-1 )
           lowercase				:	Tuple			      = -score / std

           # compute
           lowercase				:	Optional[int]			      = -1.0 / len(self.timesteps )

           lowercase				:	Optional[Any]			      = self.config.beta_min + t * (self.config.beta_max - self.config.beta_min)
           lowercase				:	str			      = beta_t.flatten()
           while len(beta_t.shape ) < len(x.shape ):
                  lowercase				:	Dict			      = beta_t.unsqueeze(-1 )
           lowercase				:	Dict			      = -0.5 * beta_t * x

           lowercase				:	int			      = torch.sqrt(lowerCamelCase__ )
           lowercase				:	List[str]			      = drift - diffusion**2 * score
           lowercase				:	Dict			      = x + drift * dt

           # add noise
           lowercase				:	Tuple			      = randn_tensor(x.shape						,layout=x.layout						,generator=lowerCamelCase__						,device=x.device						,dtype=x.dtype )
           lowercase				:	Optional[Any]			      = x_mean + diffusion * math.sqrt(-dt ) * noise

           return x, x_mean
    def __len__(    self ):



           '''simple docstring'''







           return self.config.num_train_timesteps





'''simple docstring'''
from math import ceil






def A__       (	UpperCAmelCase_ = 1_0_0_1				):
						_UpperCamelCase   :						int												=  1

						for i in range(1    ,    int(ceil(n / 2.0				)				)				):
												_UpperCamelCase   :						Dict												=  2 * i + 1
												_UpperCamelCase   :						Tuple												=  2 * i
												_UpperCamelCase   :						Any												=  total + 4 * odd**2 - 6 * even

						return total


if __name__ == "__main__":
					import sys

					if len(sys.argv) == 1:
										print(solution())
					else:
										try:
															snake_case_					:      Tuple    			=    int(sys.argv[1])
															print(solution(n))
										except ValueError:
															print('Invalid entry - please enter a number')


