





import math
from collections import defaultdict
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 KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput

def   __snake_case    (       _lowerCAmelCase			:			Union[str, Any]					,					_lowerCAmelCase			:			List[str]=0.9_99					,					_lowerCAmelCase			:			Any="cosine"					,					)			->    int:
   if alpha_transform_type == "cosine":

      def alpha_bar_fn(_lowerCAmelCase			:			Dict						):
         return math.cos((t + 0.0_08) / 1.0_08 * math.pi / 2						) ** 2

   elif alpha_transform_type == "exp":

      def alpha_bar_fn(_lowerCAmelCase			:			Tuple						):
         return math.exp(t * -12.0						)

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

   A_       :					Tuple        =      []
   for i in range(_lowerCAmelCase						):
      A_       :					Optional[int]        =      i / num_diffusion_timesteps
      A_       :					int        =      (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        __magic_name__	(				lowerCamelCase__     ,					lowerCamelCase__				):





     """simple docstring"""



     __UpperCamelCase            =  [e.name for e in KarrasDiffusionSchedulers]
     __UpperCamelCase            =  2



     @register_to_config
     def __init__(				self							:Dict      ,   snake_case							:int = 1_000      ,   snake_case							:float = 0.00085      ,   snake_case							:float = 0.012      ,   snake_case							:str = "linear"      ,   snake_case							:Optional[Union[np.ndarray, List[float]]] = None      ,   snake_case							:str = "epsilon"      ,   snake_case							:str = "linspace"      ,   snake_case							:int = 0      ,   ):





        '''simple docstring'''




        if trained_betas is not None:
           A_       :					str        =      torch.tensor(snake_case      ,   dtype=torch.floataa	)
        elif beta_schedule == "linear":
           A_       :					Tuple        =      torch.linspace(snake_case      ,   snake_case      ,   snake_case      ,   dtype=torch.floataa	)
        elif beta_schedule == "scaled_linear":
           # this schedule is very specific to the latent diffusion model.
           A_       :					Optional[Any]        =      (
               torch.linspace(beta_start**0.5      ,   beta_end**0.5      ,   snake_case      ,   dtype=torch.floataa	) ** 2
           )
        elif beta_schedule == "squaredcos_cap_v2":
           # Glide cosine schedule
           A_       :					Union[str, Any]        =      betas_for_alpha_bar(snake_case	)
        else:
           raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}"	)

        A_       :					Optional[int]        =      1.0 - self.betas
        A_       :					Dict        =      torch.cumprod(self.alphas      ,   dim=0	)

        #  set all values
        self.set_timesteps(snake_case      ,   snake_case      ,   snake_case	)



     def     SCREAMING_SNAKE_CASE		(				self							:List[str]      ,   snake_case							:List[Any]      ,   snake_case							:int=None	):





        '''simple docstring'''




        if schedule_timesteps is None:
           A_       :					Optional[int]        =      self.timesteps

        A_       :					List[str]        =      (schedule_timesteps == timestep).nonzero()

        # The sigma index that is taken for the **very** first `step`
        # is always the second index (or the last index if there is only 1)
        # This way we can ensure we don't accidentally skip a sigma in
        # case we start in the middle of the denoising schedule (e.g. for image-to-image)
        if len(self._index_counter	) == 0:
           A_       :					List[str]        =      1 if len(snake_case	) > 1 else 0
        else:
           A_       :					List[Any]        =      timestep.cpu().item() if torch.is_tensor(snake_case	) else timestep
           A_       :					Union[str, Any]        =      self._index_counter[timestep_int]

        return indices[pos].item()



     @property
     def     SCREAMING_SNAKE_CASE		(				self							:int	):





        '''simple docstring'''




        if self.config.timestep_spacing in ["linspace", "trailing"]:
           return self.sigmas.max()

        return (self.sigmas.max() ** 2 + 1) ** 0.5



     def     SCREAMING_SNAKE_CASE		(				self							:Dict      ,   snake_case							:torch.FloatTensor      ,   snake_case							:Union[float, torch.FloatTensor]      ,   ):





        '''simple docstring'''




        A_       :					str        =      self.index_for_timestep(snake_case	)

        if self.state_in_first_order:
           A_       :					Union[str, Any]        =      self.sigmas[step_index]
        else:
           A_       :					Union[str, Any]        =      self.sigmas_interpol[step_index]

        A_       :					Optional[int]        =      sample / ((sigma**2 + 1) ** 0.5)
        return sample



     def     SCREAMING_SNAKE_CASE		(				self							:Any      ,   snake_case							:int      ,   snake_case							:Union[str, torch.device] = None      ,   snake_case							:Optional[int] = None      ,   ):





        '''simple docstring'''




        A_       :					Any        =      num_inference_steps

        A_       :					str        =      num_train_timesteps or self.config.num_train_timesteps

        # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
        if self.config.timestep_spacing == "linspace":
           A_       :					Optional[int]        =      np.linspace(0      ,   num_train_timesteps - 1      ,   snake_case      ,   dtype=snake_case	)[::-1].copy()
        elif self.config.timestep_spacing == "leading":
           A_       :					Optional[Any]        =      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_       :					Dict        =      (np.arange(0      ,   snake_case	) * step_ratio).round()[::-1].copy().astype(snake_case	)
           timesteps += self.config.steps_offset
        elif self.config.timestep_spacing == "trailing":
           A_       :					List[str]        =      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_       :					Union[str, Any]        =      (np.arange(snake_case      ,   0      ,   -step_ratio	)).round().copy().astype(snake_case	)
           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_       :					Optional[Any]        =      np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5	)
        A_       :					Any        =      torch.from_numpy(np.log(snake_case	)	).to(snake_case	)

        A_       :					List[str]        =      np.interp(snake_case      ,   np.arange(0      ,   len(snake_case	)	)      ,   snake_case	)
        A_       :					int        =      np.concatenate([sigmas, [0.0]]	).astype(np.floataa	)
        A_       :					Optional[Any]        =      torch.from_numpy(snake_case	).to(device=snake_case	)

        # interpolate sigmas
        A_       :					Optional[int]        =      sigmas.log().lerp(sigmas.roll(1	).log()      ,   0.5	).exp()

        A_       :					str        =      torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2	), sigmas[-1:]]	)
        A_       :					Dict        =      torch.cat(
            [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2	), sigmas_interpol[-1:]]	)

        if str(snake_case	).startswith("mps"	):
           # mps does not support float64
           A_       :					int        =      torch.from_numpy(snake_case	).to(snake_case      ,   dtype=torch.floataa	)
        else:
           A_       :					Union[str, Any]        =      torch.from_numpy(snake_case	).to(snake_case	)

        # interpolate timesteps
        A_       :					List[Any]        =      self.sigma_to_t(snake_case	).to(snake_case      ,   dtype=timesteps.dtype	)
        A_       :					Union[str, Any]        =      torch.stack((timesteps_interpol[1:-1, None], timesteps[1:, None])      ,   dim=-1	).flatten()

        A_       :					Tuple        =      torch.cat([timesteps[:1], interleaved_timesteps]	)

        A_       :					List[Any]        =      None

        # for exp beta schedules, such as the one for `pipeline_shap_e.py`
        # we need an index counter
        A_       :					Any        =      defaultdict(snake_case	)



     def     SCREAMING_SNAKE_CASE		(				self							:Union[str, Any]      ,   snake_case							:Any	):





        '''simple docstring'''




        A_       :					Optional[Any]        =      sigma.log()

        # get distribution
        A_       :					Tuple        =      log_sigma - self.log_sigmas[:, None]

        # get sigmas range
        A_       :					Union[str, Any]        =      dists.ge(0	).cumsum(dim=0	).argmax(dim=0	).clamp(max=self.log_sigmas.shape[0] - 2	)
        A_       :					List[Any]        =      low_idx + 1

        A_       :					Dict        =      self.log_sigmas[low_idx]
        A_       :					Any        =      self.log_sigmas[high_idx]

        # interpolate sigmas
        A_       :					List[Any]        =      (low - log_sigma) / (low - high)
        A_       :					str        =      w.clamp(0      ,   1	)

        # transform interpolation to time range
        A_       :					int        =      (1 - w) * low_idx + w * high_idx
        A_       :					Union[str, Any]        =      t.view(sigma.shape	)
        return t



     @property
     def     SCREAMING_SNAKE_CASE		(				self							:Dict	):





        '''simple docstring'''




        return self.sample is None



     def     SCREAMING_SNAKE_CASE		(				self							:int      ,   snake_case							:Union[torch.FloatTensor, np.ndarray]      ,   snake_case							:Union[float, torch.FloatTensor]      ,   snake_case							:Union[torch.FloatTensor, np.ndarray]      ,   snake_case							:bool = True      ,   ):





        '''simple docstring'''




        A_       :					Any        =      self.index_for_timestep(snake_case	)

        # advance index counter by 1
        A_       :					str        =      timestep.cpu().item() if torch.is_tensor(snake_case	) else timestep
        self._index_counter[timestep_int] += 1

        if self.state_in_first_order:
           A_       :					Tuple        =      self.sigmas[step_index]
           A_       :					Optional[Any]        =      self.sigmas_interpol[step_index + 1]
           A_       :					Optional[int]        =      self.sigmas[step_index + 1]
        else:
           # 2nd order / KDPM2's method
           A_       :					List[str]        =      self.sigmas[step_index - 1]
           A_       :					Any        =      self.sigmas_interpol[step_index]
           A_       :					Union[str, Any]        =      self.sigmas[step_index]

        # currently only gamma=0 is supported. This usually works best anyways.
        # We can support gamma in the future but then need to scale the timestep before
        # passing it to the model which requires a change in API
        A_       :					Dict        =      0
        A_       :					Optional[Any]        =      sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

        # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
        if self.config.prediction_type == "epsilon":
           A_       :					List[Any]        =      sigma_hat if self.state_in_first_order else sigma_interpol
           A_       :					Optional[int]        =      sample - sigma_input * model_output
        elif self.config.prediction_type == "v_prediction":
           A_       :					int        =      sigma_hat if self.state_in_first_order else sigma_interpol
           A_       :					Optional[Any]        =      model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
               sample / (sigma_input**2 + 1)
           )
        elif self.config.prediction_type == "sample":
           raise NotImplementedError("prediction_type not implemented yet: sample"	)
        else:
           raise ValueError(
               f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"	)

        if self.state_in_first_order:
           # 2. Convert to an ODE derivative for 1st order
           A_       :					Tuple        =      (sample - pred_original_sample) / sigma_hat
           # 3. delta timestep
           A_       :					str        =      sigma_interpol - sigma_hat

           # store for 2nd order step
           A_       :					Tuple        =      sample
        else:
           # DPM-Solver-2
           # 2. Convert to an ODE derivative for 2nd order
           A_       :					List[Any]        =      (sample - pred_original_sample) / sigma_interpol

           # 3. delta timestep
           A_       :					List[Any]        =      sigma_next - sigma_hat

           A_       :					Optional[Any]        =      self.sample
           A_       :					List[str]        =      None

        A_       :					Any        =      sample + derivative * dt

        if not return_dict:
           return (prev_sample,)

        return SchedulerOutput(prev_sample=snake_case	)



     def     SCREAMING_SNAKE_CASE		(				self							:int      ,   snake_case							:torch.FloatTensor      ,   snake_case							:torch.FloatTensor      ,   snake_case							:torch.FloatTensor      ,   ):





        '''simple docstring'''




        A_       :					Dict        =      self.sigmas.to(device=original_samples.device      ,   dtype=original_samples.dtype	)
        if original_samples.device.type == "mps" and torch.is_floating_point(snake_case	):
           # mps does not support float64
           A_       :					Any        =      self.timesteps.to(original_samples.device      ,   dtype=torch.floataa	)
           A_       :					List[str]        =      timesteps.to(original_samples.device      ,   dtype=torch.floataa	)
        else:
           A_       :					List[str]        =      self.timesteps.to(original_samples.device	)
           A_       :					List[str]        =      timesteps.to(original_samples.device	)

        A_       :					Dict        =      [self.index_for_timestep(snake_case      ,   snake_case	) for t in timesteps]

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

        A_       :					Dict        =      original_samples + noise * sigma
        return noisy_samples





     def __len__(				self							:str	):





        '''simple docstring'''




        return self.config.num_train_timesteps







from math import sqrt

def   __snake_case    (       _lowerCAmelCase			:			int						)			->    bool:

   if 1 < number < 4:
      # 2 and 3 are primes
      return True
   elif number < 2 or number % 2 == 0 or number % 3 == 0:
      # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
      return False

   # All primes number are in format of 6k +/- 1
   for i in range(5					,					int(sqrt(_lowerCAmelCase						) + 1						)					,					6						):
      if number % i == 0 or number % (i + 2) == 0:
         return False
   return True

def   __snake_case    (       _lowerCAmelCase			:			int = 10001						)			->    int:
   A_       :					Any        =      0
   A_       :					Tuple        =      1
   while count != nth and number < 3:
      number += 1
      if is_prime(_lowerCAmelCase						):
         count += 1
   while count != nth:
      number += 2
      if is_prime(_lowerCAmelCase						):
         count += 1
   return number


if __name__ == "__main__":
 print(F'''{solution() = }''')
