






"""simple docstring"""


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 ..utils import randn_tensor
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput



def    lowerCAmelCase							(       __UpperCamelCase						,			__UpperCamelCase=0.999						,			__UpperCamelCase="cosine"						,			):




  """simple docstring"""







  if alpha_transform_type == "cosine":

    def alpha_bar_fn(__UpperCamelCase					):
      return math.cos((t + 0.008) / 1.008 * math.pi / 2					) ** 2

  elif alpha_transform_type == "exp":

    def alpha_bar_fn(__UpperCamelCase					):
      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    snake_case						(				a__  ,      a__		):


   '''simple docstring'''

   A_		:      int							=					[e.name for e in KarrasDiffusionSchedulers]
   A_		:      List[Any]							=					2


   @register_to_config
   def __init__(      self					:	Dict,			_lowerCamelCase					:	List[str] = 10_00,			_lowerCamelCase					:	Optional[Any] = 0.0_00_85,			_lowerCamelCase					:	int = 0.0_12,			_lowerCamelCase					:	Union[str, Any] = "linear",			_lowerCamelCase					:	Dict = None,			_lowerCamelCase					:	Union[str, Any] = "epsilon",			_lowerCamelCase					:	List[str] = "linspace",			_lowerCamelCase					:	List[Any] = 0,			):

     '''simple docstring'''
     if trained_betas is not None:
       __A		     =					torch.tensor(__UpperCAmelCase,			dtype=torch.floataa    )
     elif beta_schedule == "linear":
       __A		     =					torch.linspace(__UpperCAmelCase,			__UpperCAmelCase,			__UpperCAmelCase,			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,			__UpperCAmelCase,			dtype=torch.floataa    ) ** 2
       )
     elif beta_schedule == "squaredcos_cap_v2":
       # Glide cosine schedule
       __A		     =					betas_for_alpha_bar(__UpperCAmelCase    )
     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    )

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


   def 							_SCREAMING_SNAKE_CASE							(      self					:	Optional[int],			_lowerCamelCase					:	int,			_lowerCamelCase					:	Any=None    ):

     '''simple docstring'''
     if schedule_timesteps is None:
       __A		     =					self.timesteps

     __A		     =					(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		     =					1 if len(__UpperCAmelCase    ) > 1 else 0
     else:
       __A		     =					timestep.cpu().item() if torch.is_tensor(__UpperCAmelCase    ) else timestep
       __A		     =					self._index_counter[timestep_int]

     return indices[pos].item()


   @property
   def 							_SCREAMING_SNAKE_CASE							(      self					:	List[str]    ):

     '''simple docstring'''
     # 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 							_SCREAMING_SNAKE_CASE							(      self					:	str,			_lowerCamelCase					:	str,			_lowerCamelCase					:	Union[str, Any],			):

     '''simple docstring'''
     __A		     =					self.index_for_timestep(__UpperCAmelCase    )

     if self.state_in_first_order:
       __A		     =					self.sigmas[step_index]
     else:
       __A		     =					self.sigmas_interpol[step_index - 1]

     __A		     =					sample / ((sigma**2 + 1) ** 0.5)
     return sample


   def 							_SCREAMING_SNAKE_CASE							(      self					:	Union[str, Any],			_lowerCamelCase					:	int,			_lowerCamelCase					:	List[str] = None,			_lowerCamelCase					:	Dict = None,			):

     '''simple docstring'''
     __A		     =					num_inference_steps

     __A		     =					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		     =					np.linspace(0,			num_train_timesteps - 1,			__UpperCAmelCase,			dtype=__UpperCAmelCase    )[::-1].copy()
     elif self.config.timestep_spacing == "leading":
       __A		     =					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,			__UpperCAmelCase    ) * step_ratio).round()[::-1].copy().astype(__UpperCAmelCase    )
       timesteps += self.config.steps_offset
     elif self.config.timestep_spacing == "trailing":
       __A		     =					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(__UpperCAmelCase,			0,			-step_ratio    )).round().copy().astype(__UpperCAmelCase    )
       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		     =					torch.from_numpy(np.log(__UpperCAmelCase    )    ).to(__UpperCAmelCase    )

     __A		     =					np.interp(__UpperCAmelCase,			np.arange(0,			len(__UpperCAmelCase    )    ),			__UpperCAmelCase    )
     __A		     =					np.concatenate([sigmas, [0.0]]    ).astype(np.floataa    )
     __A		     =					torch.from_numpy(__UpperCAmelCase    ).to(device=__UpperCAmelCase    )

     # compute up and down sigmas
     __A		     =					sigmas.roll(-1    )
     __A		     =					0.0
     __A		     =					(sigmas_next**2 * (sigmas**2 - sigmas_next**2) / sigmas**2) ** 0.5
     __A		     =					(sigmas_next**2 - sigmas_up**2) ** 0.5
     __A		     =					0.0

     # compute interpolated sigmas
     __A		     =					sigmas.log().lerp(sigmas_down.log(),			0.5    ).exp()
     __A		     =					0.0

     # set sigmas
     __A		     =					torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2    ), sigmas[-1:]]    )
     __A		     =					torch.cat(
         [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2    ), sigmas_interpol[-1:]]    )
     __A		     =					torch.cat([sigmas_up[:1], sigmas_up[1:].repeat_interleave(2    ), sigmas_up[-1:]]    )
     __A		     =					torch.cat([sigmas_down[:1], sigmas_down[1:].repeat_interleave(2    ), sigmas_down[-1:]]    )

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

     __A		     =					self.sigma_to_t(__UpperCAmelCase    ).to(__UpperCAmelCase,			dtype=timesteps.dtype    )
     __A		     =					torch.stack((timesteps_interpol[:-2, None], timesteps[1:, None]),			dim=-1    ).flatten()

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

     __A		     =					None

     # for exp beta schedules, such as the one for `pipeline_shap_e.py`
     # we need an index counter
     __A		     =					defaultdict(__UpperCAmelCase    )


   def 							_SCREAMING_SNAKE_CASE							(      self					:	Union[str, Any],			_lowerCamelCase					:	str    ):

     '''simple docstring'''
     # get log sigma
     __A		     =					sigma.log()

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

     # get sigmas range
     __A		     =					dists.ge(0    ).cumsum(dim=0    ).argmax(dim=0    ).clamp(max=self.log_sigmas.shape[0] - 2    )
     __A		     =					low_idx + 1

     __A		     =					self.log_sigmas[low_idx]
     __A		     =					self.log_sigmas[high_idx]

     # interpolate sigmas
     __A		     =					(low - log_sigma) / (low - high)
     __A		     =					w.clamp(0,			1    )

     # transform interpolation to time range
     __A		     =					(1 - w) * low_idx + w * high_idx
     __A		     =					t.view(sigma.shape    )
     return t


   @property
   def 							_SCREAMING_SNAKE_CASE							(      self					:	Optional[int]    ):

     '''simple docstring'''
     return self.sample is None


   def 							_SCREAMING_SNAKE_CASE							(      self					:	Optional[int],			_lowerCamelCase					:	List[str],			_lowerCamelCase					:	int,			_lowerCamelCase					:	List[Any],			_lowerCamelCase					:	Tuple = None,			_lowerCamelCase					:	List[str] = True,			):

     '''simple docstring'''
     __A		     =					self.index_for_timestep(__UpperCAmelCase    )

     # advance index counter by 1
     __A		     =					timestep.cpu().item() if torch.is_tensor(__UpperCAmelCase    ) else timestep
     self._index_counter[timestep_int] += 1

     if self.state_in_first_order:
       __A		     =					self.sigmas[step_index]
       __A		     =					self.sigmas_interpol[step_index]
       __A		     =					self.sigmas_up[step_index]
       __A		     =					self.sigmas_down[step_index - 1]
     else:
       # 2nd order / KPDM2's method
       __A		     =					self.sigmas[step_index - 1]
       __A		     =					self.sigmas_interpol[step_index - 1]
       __A		     =					self.sigmas_up[step_index - 1]
       __A		     =					self.sigmas_down[step_index - 1]

     # 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		     =					0
     __A		     =					sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

     __A		     =					model_output.device
     __A		     =					randn_tensor(model_output.shape,			dtype=model_output.dtype,			device=__UpperCAmelCase,			generator=__UpperCAmelCase    )

     # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
     if self.config.prediction_type == "epsilon":
       __A		     =					sigma_hat if self.state_in_first_order else sigma_interpol
       __A		     =					sample - sigma_input * model_output
     elif self.config.prediction_type == "v_prediction":
       __A		     =					sigma_hat if self.state_in_first_order else sigma_interpol
       __A		     =					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		     =					(sample - pred_original_sample) / sigma_hat
       # 3. delta timestep
       __A		     =					sigma_interpol - sigma_hat

       # store for 2nd order step
       __A		     =					sample
       __A		     =					dt
       __A		     =					sample + derivative * dt
     else:
       # DPM-Solver-2
       # 2. Convert to an ODE derivative for 2nd order
       __A		     =					(sample - pred_original_sample) / sigma_interpol
       # 3. delta timestep
       __A		     =					sigma_down - sigma_hat

       __A		     =					self.sample
       __A		     =					None

       __A		     =					sample + derivative * dt
       __A		     =					prev_sample + noise * sigma_up

     if not return_dict:
       return (prev_sample,)

     return SchedulerOutput(prev_sample=__UpperCAmelCase    )


   def 							_SCREAMING_SNAKE_CASE							(      self					:	Union[str, Any],			_lowerCamelCase					:	Dict,			_lowerCamelCase					:	Dict,			_lowerCamelCase					:	Optional[Any],			):

     '''simple docstring'''
     # 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(__UpperCAmelCase    ):
       # 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		     =					[self.index_for_timestep(__UpperCAmelCase,			__UpperCAmelCase    ) 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					:	List[str]    ):

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








"""simple docstring"""






def    A_ ( _lowerCAmelCase  :       str,  _lowerCAmelCase  :       str							):






     """simple docstring"""

     if len(_lowerCAmelCase							) < len(_lowerCAmelCase							):
          return levenshtein_distance(_lowerCAmelCase,  _lowerCAmelCase							)

     if len(_lowerCAmelCase							) == 0:
          return len(_lowerCAmelCase							)

     _a     						=					list(range(len(_lowerCAmelCase							) + 1							)							)

     for i, ca in enumerate(_lowerCAmelCase							):
          _a     						=					[i + 1]

          for j, ca in enumerate(_lowerCAmelCase							):
               # Calculate insertions, deletions and substitutions
               _a     						=					previous_row[j + 1] + 1
               _a     						=					current_row[j] + 1
               _a     						=					previous_row[j] + (ca != ca)

               # Get the minimum to append to the current row
               current_row.append(min(_lowerCAmelCase,  _lowerCAmelCase,  _lowerCAmelCase							)							)

          # Store the previous row
          _a     						=					current_row

     # Returns the last element (distance)
     return previous_row[-1]


if __name__ == "__main__":
   __snake_case												=							input('''Enter the first word:\n''').strip()
   __snake_case												=							input('''Enter the second word:\n''').strip()

   __snake_case												=							levenshtein_distance(first_word, second_word)
   print(f'Levenshtein distance between {first_word} and {second_word} is {result}')