




from math import asin, atan, cos, radians, sin, sqrt, tan

_snake_case										=       6_3_7_8_1_3_7.0
_snake_case										=       6_3_5_6_7_5_2.3_1_4_2_4_5
_snake_case										=       6378137







def 				lowerCAmelCase_	(     snake_case_,snake_case_,snake_case_,snake_case_     ):
      _A							:     Any			=						(AXIS_A - AXIS_B) / AXIS_A
      _A							:     Optional[int]			=						atan((1 - flattening) * tan(radians(snake_case_     )     )     )
      _A							:     List[str]			=						atan((1 - flattening) * tan(radians(snake_case_     )     )     )
      _A							:     Optional[Any]			=						radians(snake_case_     )
      _A							:     str			=						radians(snake_case_     )
      # Equation
      _A							:     Dict			=						sin((phi_a - phi_a) / 2     )
      _A							:     List[str]			=						sin((lambda_a - lambda_a) / 2     )
      # Square both values
      sin_sq_phi *= sin_sq_phi
      sin_sq_lambda *= sin_sq_lambda
      _A							:     Optional[int]			=						sqrt(sin_sq_phi + (cos(snake_case_     ) * cos(snake_case_     ) * sin_sq_lambda)     )
      return 2 * RADIUS * asin(snake_case_     )


if __name__ == "__main__":
  import doctest

  doctest.testmod()







# DISCLAIMER: This file is strongly influenced by https://github.com/yang-song/score_sde_pytorch

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 						lowercase							(   UpperCamelCase__,UpperCamelCase__		):
     _a							 =						1

     @register_to_config
     def __init__(  self		,     _a=2000		,     _a=0.1		,     _a=20		,     _a=1e-3				)						->							List[Any]:
           _A							:     Dict			=						None
           _A							:     List[Any]			=						None
           _A							:     Dict			=						None

     def 					a__	(  self		,     _a		,     _a = None				)						->							Union[str, Any]:
           _A							:     Union[str, Any]			=						torch.linspace(1		,     self.config.sampling_eps		,     _a		,     device=_a				)

     def 					a__	(  self		,     _a		,     _a		,     _a		,     _a=None				)						->							Dict:
           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
           _A							:     Any			=						(
               -0.25 * t**2 * (self.config.beta_max - self.config.beta_min) - 0.5 * t * self.config.beta_min
           )
           _A							:     List[Any]			=						torch.sqrt(1.0 - torch.exp(2.0 * log_mean_coeff				)				)
           _A							:     List[str]			=						std.flatten()
           while len(std.shape				) < len(score.shape				):
                 _A							:     List[Any]			=						std.unsqueeze(-1				)
           _A							:     int			=						-score / std

           # compute
           _A							:     Tuple			=						-1.0 / len(self.timesteps				)

           _A							:     str			=						self.config.beta_min + t * (self.config.beta_max - self.config.beta_min)
           _A							:     List[str]			=						beta_t.flatten()
           while len(beta_t.shape				) < len(x.shape				):
                 _A							:     Union[str, Any]			=						beta_t.unsqueeze(-1				)
           _A							:     Tuple			=						-0.5 * beta_t * x

           _A							:     Tuple			=						torch.sqrt(_a				)
           _A							:     Dict			=						drift - diffusion**2 * score
           _A							:     Dict			=						x + drift * dt

           # add noise
           _A							:     Any			=						randn_tensor(x.shape		,     layout=x.layout		,     generator=_a		,     device=x.device		,     dtype=x.dtype				)
           _A							:     str			=						x_mean + diffusion * math.sqrt(-dt				) * noise

           return x, x_mean



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

