



'''simple docstring'''





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

import numpy as np
import torch

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


A__  :					List[str]				= logging.get_logger(__name__)  # pylint: disable=invalid-name



@dataclass
class       snake_case__		(  _lowerCAmelCase							):
 A__							=      42



class       snake_case__		(  _lowerCAmelCase   ,			_lowerCAmelCase							):
 A__							=      1
 @register_to_config
 def __init__(					self		:				List[Any]	,			__a		:				int = 40	,			__a		:				float = 0.0_0_2	,			__a		:				float = 8_0.0	,			__a		:				float = 0.5	,			__a		:				float = 1.0	,			__a		:				float = 7.0	,			__a		:				bool = True	,			)	->					List[str]:







       '''simple docstring'''
       __snake_case      :					str						=  sigma_max

       __snake_case      :					Dict						=  np.linspace(0	,			1	,			lowerCAmelCase__   )
       __snake_case      :					Tuple						=  self._convert_to_karras(lowerCAmelCase__   )
       __snake_case      :					int						=  self.sigma_to_t(lowerCAmelCase__   )

       # setable values
       __snake_case      :					Optional[Any]						=  None
       __snake_case      :					Optional[Any]						=  torch.from_numpy(lowerCAmelCase__   )
       __snake_case      :					Dict						=  torch.from_numpy(lowerCAmelCase__   )
       __snake_case      :					Any						=  False
       __snake_case      :					str						=  False
 def A_					(					self		:				Optional[Any]	,			__a		:				Any	,			__a		:				List[str]=None   )	->					str:







       '''simple docstring'''



       if schedule_timesteps is None:
             __snake_case      :					Dict						=  self.timesteps

       __snake_case      :					Union[str, Any]						=  (schedule_timesteps == timestep).nonzero()
       return indices.item()
 def A_					(					self		:				Any	,			__a		:				torch.FloatTensor	,			__a		:				Union[float, torch.FloatTensor]   )	->					torch.FloatTensor:







       '''simple docstring'''



       if isinstance(lowerCAmelCase__	,			torch.Tensor   ):
             __snake_case      :					Union[str, Any]						=  timestep.to(self.timesteps.device   )
       __snake_case      :					Dict						=  self.index_for_timestep(lowerCAmelCase__   )
       __snake_case      :					int						=  self.sigmas[step_idx]

       __snake_case      :					Tuple						=  sample / ((sigma**2 + self.config.sigma_data**2) ** 0.5)

       __snake_case      :					List[Any]						=  True
       return sample
 def A_					(					self		:				Any	,			__a		:				Union[float, np.ndarray]   )	->					Optional[int]:







       '''simple docstring'''



       if not isinstance(lowerCAmelCase__	,			np.ndarray   ):
             __snake_case      :					Dict						=  np.array(lowerCAmelCase__	,			dtype=np.floataa   )

       __snake_case      :					List[str]						=  1000 * 0.2_5 * np.log(sigmas + 1e-44   )

       return timesteps
 def A_					(					self		:				Union[str, Any]	,			__a		:				Optional[int] = None	,			__a		:				Union[str, torch.device] = None	,			__a		:				Optional[List[int]] = None	,			)	->					Any:







       '''simple docstring'''



       if num_inference_steps is None and timesteps is None:
             raise ValueError('Exactly one of `num_inference_steps` or `timesteps` must be supplied.'   )

       if num_inference_steps is not None and timesteps is not None:
             raise ValueError('Can only pass one of `num_inference_steps` or `timesteps`.'   )

       # Follow DDPMScheduler custom timesteps logic
       if timesteps is not None:
             for i in range(1	,			len(lowerCAmelCase__   )   ):
                   if timesteps[i] >= timesteps[i - 1]:
                         raise ValueError('`timesteps` must be in descending order.'   )

             if timesteps[0] >= self.config.num_train_timesteps:
                   raise ValueError(
                       f'''`timesteps` must start before `self.config.train_timesteps`:'''
                       f''' {self.config.num_train_timesteps}.'''   )

             __snake_case      :					Any						=  np.array(lowerCAmelCase__	,			dtype=np.intaa   )
             __snake_case      :					int						=  True
       else:
             if num_inference_steps > self.config.num_train_timesteps:
                   raise ValueError(
                       f'''`num_inference_steps`: {num_inference_steps} cannot be larger than `self.config.train_timesteps`:'''
                       f''' {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle'''
                       f''' maximal {self.config.num_train_timesteps} timesteps.'''   )

             __snake_case      :					int						=  num_inference_steps

             __snake_case      :					str						=  self.config.num_train_timesteps // self.num_inference_steps
             __snake_case      :					List[str]						=  (np.arange(0	,			lowerCAmelCase__   ) * step_ratio).round()[::-1].copy().astype(np.intaa   )
             __snake_case      :					Tuple						=  False

       # Map timesteps to Karras sigmas directly for multistep sampling
       # See https://github.com/openai/consistency_models/blob/main/cm/karras_diffusion.py#L675
       __snake_case      :					Optional[Any]						=  self.config.num_train_timesteps
       __snake_case      :					List[str]						=  timesteps[::-1].copy()
       __snake_case      :					Optional[Any]						=  ramp / (num_train_timesteps - 1)
       __snake_case      :					Dict						=  self._convert_to_karras(lowerCAmelCase__   )
       __snake_case      :					str						=  self.sigma_to_t(lowerCAmelCase__   )

       __snake_case      :					int						=  np.concatenate([sigmas, [self.sigma_min]]   ).astype(np.floataa   )
       __snake_case      :					List[str]						=  torch.from_numpy(lowerCAmelCase__   ).to(device=lowerCAmelCase__   )

       if str(lowerCAmelCase__   ).startswith('mps'   ):
             # mps does not support float64
             __snake_case      :					Dict						=  torch.from_numpy(lowerCAmelCase__   ).to(lowerCAmelCase__	,			dtype=torch.floataa   )
       else:
             __snake_case      :					Tuple						=  torch.from_numpy(lowerCAmelCase__   ).to(device=lowerCAmelCase__   )
 def A_					(					self		:				str	,			__a		:				Optional[int]   )	->					str:







       '''simple docstring'''
       __snake_case      :					float						=  self.config.sigma_min
       __snake_case      :					float						=  self.config.sigma_max

       __snake_case      :					Any						=  self.config.rho
       __snake_case      :					int						=  sigma_min ** (1 / rho)
       __snake_case      :					Tuple						=  sigma_max ** (1 / rho)
       __snake_case      :					Tuple						=  (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
       return sigmas
 def A_					(					self		:				Dict	,			__a		:				Optional[int]   )	->					Tuple:







       '''simple docstring'''
       __snake_case      :					Optional[int]						=  self.config.sigma_data

       __snake_case      :					Dict						=  sigma_data**2 / (sigma**2 + sigma_data**2)
       __snake_case      :					Dict						=  sigma * sigma_data / (sigma**2 + sigma_data**2) ** 0.5
       return c_skip, c_out
 def A_					(					self		:				List[Any]	,			__a		:				List[str]   )	->					Optional[Any]:







       '''simple docstring'''
       __snake_case      :					List[Any]						=  self.config.sigma_min
       __snake_case      :					Union[str, Any]						=  self.config.sigma_data

       __snake_case      :					List[Any]						=  sigma_data**2 / ((sigma - sigma_min) ** 2 + sigma_data**2)
       __snake_case      :					Optional[Any]						=  (sigma - sigma_min) * sigma_data / (sigma**2 + sigma_data**2) ** 0.5
       return c_skip, c_out
 def A_					(					self		:				str	,			__a		:				torch.FloatTensor	,			__a		:				Union[float, torch.FloatTensor]	,			__a		:				torch.FloatTensor	,			__a		:				Optional[torch.Generator] = None	,			__a		:				bool = True	,			)	->					Union[CMStochasticIterativeSchedulerOutput, Tuple]:







       '''simple docstring'''



       if (
           isinstance(lowerCAmelCase__	,			lowerCAmelCase__   )
           or isinstance(lowerCAmelCase__	,			torch.IntTensor   )
           or isinstance(lowerCAmelCase__	,			torch.LongTensor   )
       ):
             raise ValueError(
                 (
                     'Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to'
                     f''' `{self.__class__}.step()` is not supported. Make sure to pass'''
                     ' one of the `scheduler.timesteps` as a timestep.'
                 )	,			)

       if not self.is_scale_input_called:
             logger.warning(
                 'The `scale_model_input` function should be called before `step` to ensure correct denoising. '
                 'See `StableDiffusionPipeline` for a usage example.'   )

       if isinstance(lowerCAmelCase__	,			torch.Tensor   ):
             __snake_case      :					List[str]						=  timestep.to(self.timesteps.device   )

       __snake_case      :					Any						=  self.config.sigma_min
       __snake_case      :					List[str]						=  self.config.sigma_max

       __snake_case      :					List[Any]						=  self.index_for_timestep(lowerCAmelCase__   )

       # sigma_next corresponds to next_t in original implementation
       __snake_case      :					List[Any]						=  self.sigmas[step_index]
       if step_index + 1 < self.config.num_train_timesteps:
             __snake_case      :					Optional[int]						=  self.sigmas[step_index + 1]
       else:
             # Set sigma_next to sigma_min
             __snake_case      :					List[str]						=  self.sigmas[-1]

       # Get scalings for boundary conditions
       __snake_case      :					Union[str, Any]						=  self.get_scalings_for_boundary_condition(lowerCAmelCase__   )

       # 1. Denoise model output using boundary conditions
       __snake_case      :					Union[str, Any]						=  c_out * model_output + c_skip * sample
       if self.config.clip_denoised:
             __snake_case      :					Tuple						=  denoised.clamp(-1	,			1   )

       # 2. Sample z ~ N(0, s_noise^2 * I)
       # Noise is not used for onestep sampling.
       if len(self.timesteps   ) > 1:
             __snake_case      :					int						=  randn_tensor(
                 model_output.shape	,			dtype=model_output.dtype	,			device=model_output.device	,			generator=lowerCAmelCase__   )
       else:
             __snake_case      :					int						=  torch.zeros_like(lowerCAmelCase__   )
       __snake_case      :					List[Any]						=  noise * self.config.s_noise

       __snake_case      :					List[Any]						=  sigma_next.clamp(min=lowerCAmelCase__	,			max=lowerCAmelCase__   )

       # 3. Return noisy sample
       # tau = sigma_hat, eps = sigma_min
       __snake_case      :					Optional[Any]						=  denoised + z * (sigma_hat**2 - sigma_min**2) ** 0.5

       if not return_dict:
             return (prev_sample,)

       return CMStochasticIterativeSchedulerOutput(prev_sample=lowerCAmelCase__   )
 def A_					(					self		:				Optional[int]	,			__a		:				torch.FloatTensor	,			__a		:				torch.FloatTensor	,			__a		:				torch.FloatTensor	,			)	->					torch.FloatTensor:







       '''simple docstring'''
       __snake_case      :					Union[str, Any]						=  self.sigmas.to(device=original_samples.device	,			dtype=original_samples.dtype   )
       if original_samples.device.type == "mps" and torch.is_floating_point(lowerCAmelCase__   ):
             # mps does not support float64
             __snake_case      :					List[Any]						=  self.timesteps.to(original_samples.device	,			dtype=torch.floataa   )
             __snake_case      :					Tuple						=  timesteps.to(original_samples.device	,			dtype=torch.floataa   )
       else:
             __snake_case      :					Optional[Any]						=  self.timesteps.to(original_samples.device   )
             __snake_case      :					Dict						=  timesteps.to(original_samples.device   )

       __snake_case      :					Dict						=  [(schedule_timesteps == t).nonzero().item() for t in timesteps]

       __snake_case      :					List[str]						=  sigmas[step_indices].flatten()
       while len(sigma.shape   ) < len(original_samples.shape   ):
             __snake_case      :					Optional[Any]						=  sigma.unsqueeze(-1   )

       __snake_case      :					List[Any]						=  original_samples + noise * sigma
       return noisy_samples





 def __len__(					self		:				str   )	->					int:







       '''simple docstring'''
       return self.config.num_train_timesteps










"""simple docstring"""




def        a_				(							_lowercase = 10**6   ):

						if n <= 0:
												raise ValueError('''Please enter an integer greater than 0'''   )

						_UpperCamelCase			:					Any     =    list(range(n + 1   )   )
						for number in range(2       ,						n + 1   ):
												if phi[number] == number:
																		phi[number] -= 1
																		for multiple in range(number * 2       ,						n + 1       ,						_lowercase   ):
																								_UpperCamelCase			:					List[str]     =    (phi[multiple] // number) * (number - 1)

						_UpperCamelCase			:					Union[str, Any]     =    1
						for number in range(1       ,						n + 1   ):
												if (answer / phi[answer]) < (number / phi[number]):
																		_UpperCamelCase			:					List[str]     =    number

						return answer


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



