


'''simple docstring'''






import math
import warnings
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch
from scipy import integrate

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin




@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->LMSDiscrete
class 			a  (  _SCREAMING_SNAKE_CASE							):
 _lowerCAmelCase			       =						42
 _lowerCAmelCase			       =						None






def 						_A					(lowerCAmelCase__	:Optional[Any]					,    lowerCAmelCase__	:Dict=0.9_9_9					,    lowerCAmelCase__	:Dict="cosine"					,    ) ->	Dict:




     '''simple docstring'''



     if alpha_transform_type == "cosine":

          def alpha_bar_fn(lowerCAmelCase__	:Dict		):
               return math.cos((t + 0.0_0_8) / 1.0_0_8 * math.pi / 2		) ** 2

     elif alpha_transform_type == "exp":

          def alpha_bar_fn(lowerCAmelCase__	:Optional[Any]		):
               return math.exp(t * -1_2.0		)

     else:
          raise ValueError(f'Unsupported alpha_tranform_type: {alpha_transform_type}'		)

     _a         =				[]
     for i in range(lowerCAmelCase__		):
          _a         =				i / num_diffusion_timesteps
          _a         =				(i + 1) / num_diffusion_timesteps
          betas.append(min(1 - alpha_bar_fn(lowerCAmelCase__		) / alpha_bar_fn(lowerCAmelCase__		)					,    lowerCAmelCase__		)		)
     return torch.tensor(lowerCAmelCase__					,    dtype=torch.floataa		)






class 			a  (  _SCREAMING_SNAKE_CASE	,					_SCREAMING_SNAKE_CASE							):
 _lowerCAmelCase			       =						[e.name for e in KarrasDiffusionSchedulers]
 _lowerCAmelCase			       =						1
 @register_to_config
 def __init__(			self   ,					__magic_name__ = 10_00   ,					__magic_name__ = 0.0_0_0_1   ,					__magic_name__ = 0.0_2   ,					__magic_name__ = "linear"   ,					__magic_name__ = None   ,					__magic_name__ = False   ,					__magic_name__ = "epsilon"   ,					__magic_name__ = "linspace"   ,					__magic_name__ = 0   ,					)       ->				Tuple:
      if trained_betas is not None:
           _a         =				torch.tensor(__magic_name__   ,					dtype=torch.floataa    )
      elif beta_schedule == "linear":
           _a         =				torch.linspace(__magic_name__   ,					__magic_name__   ,					__magic_name__   ,					dtype=torch.floataa    )
      elif beta_schedule == "scaled_linear":
           # this schedule is very specific to the latent diffusion model.
           _a         =				(
               torch.linspace(beta_start**0.5   ,					beta_end**0.5   ,					__magic_name__   ,					dtype=torch.floataa    ) ** 2
           )
      elif beta_schedule == "squaredcos_cap_v2":
           # Glide cosine schedule
           _a         =				betas_for_alpha_bar(__magic_name__    )
      else:
           raise NotImplementedError(f'{beta_schedule} does is not implemented for {self.__class__}'    )

      _a         =				1.0 - self.betas
      _a         =				torch.cumprod(self.alphas   ,					dim=0    )

      _a         =				np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5    )
      _a         =				np.concatenate([sigmas[::-1], [0.0]]    ).astype(np.floataa    )
      _a         =				torch.from_numpy(__magic_name__    )

      # setable values
      _a         =				None
      _a         =				use_karras_sigmas
      self.set_timesteps(__magic_name__   ,					__magic_name__    )
      _a         =				[]
      _a         =				False
 @property
 def 				__UpperCAmelCase		(			self    )       ->				str:
      # standard deviation of the initial noise distribution
      if self.config.timestep_spacing in ["linspace", "trailing"]:
           return self.sigmas.max()

      return (self.sigmas.max() ** 2 + 1) ** 0.5
 def 				__UpperCAmelCase		(			self   ,					__magic_name__   ,					__magic_name__    )       ->				torch.FloatTensor:
      if isinstance(__magic_name__   ,					torch.Tensor    ):
           _a         =				timestep.to(self.timesteps.device    )
      _a         =				(self.timesteps == timestep).nonzero().item()
      _a         =				self.sigmas[step_index]
      _a         =				sample / ((sigma**2 + 1) ** 0.5)
      _a         =				True
      return sample
 def 				__UpperCAmelCase		(			self   ,					__magic_name__   ,					__magic_name__   ,					__magic_name__    )       ->				Any:

      def lms_derivative(__magic_name__    ):
           _a         =				1.0
           for k in range(__magic_name__    ):
                if current_order == k:
                     continue
                prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
           return prod

      _a         =				integrate.quad(__magic_name__   ,					self.sigmas[t]   ,					self.sigmas[t + 1]   ,					epsrel=1e-4    )[0]

      return integrated_coeff
 def 				__UpperCAmelCase		(			self   ,					__magic_name__   ,					__magic_name__ = None    )       ->				List[Any]:
      _a         =				num_inference_steps

      # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
      if self.config.timestep_spacing == "linspace":
           _a         =				np.linspace(0   ,					self.config.num_train_timesteps - 1   ,					__magic_name__   ,					dtype=__magic_name__    )[
               ::-1
           ].copy()
      elif self.config.timestep_spacing == "leading":
           _a         =				self.config.num_train_timesteps // self.num_inference_steps
           # creates integer timesteps by multiplying by ratio
           # casting to int to avoid issues when num_inference_step is power of 3
           _a         =				(np.arange(0   ,					__magic_name__    ) * step_ratio).round()[::-1].copy().astype(__magic_name__    )
           timesteps += self.config.steps_offset
      elif self.config.timestep_spacing == "trailing":
           _a         =				self.config.num_train_timesteps / self.num_inference_steps
           # creates integer timesteps by multiplying by ratio
           # casting to int to avoid issues when num_inference_step is power of 3
           _a         =				(np.arange(self.config.num_train_timesteps   ,					0   ,					-step_ratio    )).round().copy().astype(__magic_name__    )
           timesteps -= 1
      else:
           raise ValueError(
               f'{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.'    )

      _a         =				np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5    )
      _a         =				np.log(__magic_name__    )
      _a         =				np.interp(__magic_name__   ,					np.arange(0   ,					len(__magic_name__    )    )   ,					__magic_name__    )

      if self.use_karras_sigmas:
           _a         =				self._convert_to_karras(in_sigmas=__magic_name__    )
           _a         =				np.array([self._sigma_to_t(__magic_name__   ,					__magic_name__    ) for sigma in sigmas]    )

      _a         =				np.concatenate([sigmas, [0.0]]    ).astype(np.floataa    )

      _a         =				torch.from_numpy(__magic_name__    ).to(device=__magic_name__    )
      if str(__magic_name__    ).startswith('mps'    ):
           # mps does not support float64
           _a         =				torch.from_numpy(__magic_name__    ).to(__magic_name__   ,					dtype=torch.floataa    )
      else:
           _a         =				torch.from_numpy(__magic_name__    ).to(device=__magic_name__    )

      _a         =				[]
 def 				__UpperCAmelCase		(			self   ,					__magic_name__   ,					__magic_name__    )       ->				Union[str, Any]:
      # get log sigma
      _a         =				np.log(__magic_name__    )

      # get distribution
      _a         =				log_sigma - log_sigmas[:, np.newaxis]

      # get sigmas range
      _a         =				np.cumsum((dists >= 0)   ,					axis=0    ).argmax(axis=0    ).clip(max=log_sigmas.shape[0] - 2    )
      _a         =				low_idx + 1

      _a         =				log_sigmas[low_idx]
      _a         =				log_sigmas[high_idx]

      # interpolate sigmas
      _a         =				(low - log_sigma) / (low - high)
      _a         =				np.clip(__magic_name__   ,					0   ,					1    )

      # transform interpolation to time range
      _a         =				(1 - w) * low_idx + w * high_idx
      _a         =				t.reshape(sigma.shape    )
      return t
 def 				__UpperCAmelCase		(			self   ,					__magic_name__    )       ->				torch.FloatTensor:
      _a         =				in_sigmas[-1].item()
      _a         =				in_sigmas[0].item()

      _a         =				7.0  # 7.0 is the value used in the paper
      _a         =				np.linspace(0   ,					1   ,					self.num_inference_steps    )
      _a         =				sigma_min ** (1 / rho)
      _a         =				sigma_max ** (1 / rho)
      _a         =				(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
      return sigmas
 def 				__UpperCAmelCase		(			self   ,					__magic_name__   ,					__magic_name__   ,					__magic_name__   ,					__magic_name__ = 4   ,					__magic_name__ = True   ,					)       ->				Union[LMSDiscreteSchedulerOutput, Tuple]:
      if not self.is_scale_input_called:
           warnings.warn(
               'The `scale_model_input` function should be called before `step` to ensure correct denoising. '
               'See `StableDiffusionPipeline` for a usage example.'    )

      if isinstance(__magic_name__   ,					torch.Tensor    ):
           _a         =				timestep.to(self.timesteps.device    )
      _a         =				(self.timesteps == timestep).nonzero().item()
      _a         =				self.sigmas[step_index]

      # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
      if self.config.prediction_type == "epsilon":
           _a         =				sample - sigma * model_output
      elif self.config.prediction_type == "v_prediction":
           # * c_out + input * c_skip
           _a         =				model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
      elif self.config.prediction_type == "sample":
           _a         =				model_output
      else:
           raise ValueError(
               f'prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`'    )

      # 2. Convert to an ODE derivative
      _a         =				(sample - pred_original_sample) / sigma
      self.derivatives.append(__magic_name__    )
      if len(self.derivatives    ) > order:
           self.derivatives.pop(0    )

      # 3. Compute linear multistep coefficients
      _a         =				min(step_index + 1   ,					__magic_name__    )
      _a         =				[self.get_lms_coefficient(__magic_name__   ,					__magic_name__   ,					__magic_name__    ) for curr_order in range(__magic_name__    )]

      # 4. Compute previous sample based on the derivatives path
      _a         =				sample + sum(
          coeff * derivative for coeff, derivative in zip(__magic_name__   ,					reversed(self.derivatives    )    )    )

      if not return_dict:
           return (prev_sample,)

      return LMSDiscreteSchedulerOutput(prev_sample=__magic_name__   ,					pred_original_sample=__magic_name__    )
 def 				__UpperCAmelCase		(			self   ,					__magic_name__   ,					__magic_name__   ,					__magic_name__   ,					)       ->				torch.FloatTensor:
      # Make sure sigmas and timesteps have the same device and dtype as original_samples
      _a         =				self.sigmas.to(device=original_samples.device   ,					dtype=original_samples.dtype    )
      if original_samples.device.type == "mps" and torch.is_floating_point(__magic_name__    ):
           # mps does not support float64
           _a         =				self.timesteps.to(original_samples.device   ,					dtype=torch.floataa    )
           _a         =				timesteps.to(original_samples.device   ,					dtype=torch.floataa    )
      else:
           _a         =				self.timesteps.to(original_samples.device    )
           _a         =				timesteps.to(original_samples.device    )

      _a         =				[(schedule_timesteps == t).nonzero().item() for t in timesteps]

      _a         =				sigmas[step_indices].flatten()
      while len(sigma.shape    ) < len(original_samples.shape    ):
           _a         =				sigma.unsqueeze(-1    )

      _a         =				original_samples + noise * sigma
      return noisy_samples




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





'''simple docstring'''






def 						_A					(lowerCAmelCase__	:int					,    lowerCAmelCase__	:int		) ->	int:




     '''simple docstring'''



     if a < b:
          return gcd(lowerCAmelCase__					,    lowerCAmelCase__		)
     if a % b == 0:
          return b
     return gcd(lowerCAmelCase__					,    a % b		)






def 						_A					(lowerCAmelCase__	:int					,    lowerCAmelCase__	:int					,    lowerCAmelCase__	:int		) ->	int:




     '''simple docstring'''



     if y == 0:
          return 1
     _a         =				power(lowerCAmelCase__					,    y // 2					,    lowerCAmelCase__		) % mod
     _a         =				(temp * temp) % mod
     if y % 2 == 1:
          _a         =				(temp * x) % mod
     return temp






def 						_A					(lowerCAmelCase__	:int		) ->	bool:




     '''simple docstring'''



     _a         =				2
     while b < n:
          if gcd(lowerCAmelCase__					,    lowerCAmelCase__		) == 1 and power(lowerCAmelCase__					,    n - 1					,    lowerCAmelCase__		) != 1:
               return False
          b += 1
     return True


if __name__ == "__main__":
 a_       :     Any 							=     int(input("Enter number: ").strip())
 if is_carmichael_number(number):
  print(f'''{number} is a Carmichael Number.''')
 else:
  print(f'''{number} is not a Carmichael Number.''')

