



"""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 .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput






def 						__UpperCAmelCase       (							snake_case_	:	Optional[Any] ,						snake_case_	:	List[str]=0.9_9_9 ,						snake_case_	:	str="cosine" ,						)				->						Dict:






   """simple docstring"""


   if alpha_transform_type == "cosine":

      def alpha_bar_fn(snake_case_	:	List[Any] ):
         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(snake_case_	:	int ):
         return math.exp(t * -12.0 )

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

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



class    __lowerCamelCase						( lowerCamelCase__ ,				lowerCamelCase__     ):
   __UpperCamelCase						= [e.name for e in KarrasDiffusionSchedulers]
   __UpperCamelCase						= 2







   @register_to_config
   def __init__(self							,						lowerCamelCase = 1_000							,						lowerCamelCase = 0.0_0085							,						lowerCamelCase = 0.012							,						lowerCamelCase = "linear"							,						lowerCamelCase = None							,						lowerCamelCase = "epsilon"							,						lowerCamelCase = "linspace"							,						lowerCamelCase = 0							,						):




      '''simple docstring'''




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

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

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







   def 				A__    (self							,						lowerCamelCase							,						lowerCamelCase=None					):




      '''simple docstring'''




      if schedule_timesteps is None:
         _lowerCAmelCase         =		self.timesteps

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

      return indices[pos].item()







   @property
   def 				A__    (self					):




      '''simple docstring'''




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

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







   def 				A__    (self							,						lowerCamelCase							,						lowerCamelCase							,						):




      '''simple docstring'''




      _lowerCAmelCase         =		self.index_for_timestep(a__					)

      if self.state_in_first_order:
         _lowerCAmelCase         =		self.sigmas[step_index]
      else:
         _lowerCAmelCase         =		self.sigmas_interpol[step_index]

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







   def 				A__    (self							,						lowerCamelCase							,						lowerCamelCase = None							,						lowerCamelCase = None							,						):




      '''simple docstring'''




      _lowerCAmelCase         =		num_inference_steps

      _lowerCAmelCase         =		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":
         _lowerCAmelCase         =		np.linspace(0							,						num_train_timesteps - 1							,						a__							,						dtype=a__					)[::-1].copy()
      elif self.config.timestep_spacing == "leading":
         _lowerCAmelCase         =		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
         _lowerCAmelCase         =		(np.arange(0							,						a__					) * step_ratio).round()[::-1].copy().astype(a__					)
         timesteps += self.config.steps_offset
      elif self.config.timestep_spacing == "trailing":
         _lowerCAmelCase         =		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
         _lowerCAmelCase         =		(np.arange(a__							,						0							,						-step_ratio					)).round().copy().astype(a__					)
         timesteps -= 1
      else:
         raise ValueError(
             f"""{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'."""					)

      _lowerCAmelCase         =		np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5					)
      _lowerCAmelCase         =		torch.from_numpy(np.log(a__					)					).to(a__					)

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

      # interpolate sigmas
      _lowerCAmelCase         =		sigmas.log().lerp(sigmas.roll(1					).log()							,						0.5					).exp()

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

      if str(a__					).startswith("""mps"""					):
         # mps does not support float64
         _lowerCAmelCase         =		torch.from_numpy(a__					).to(a__							,						dtype=torch.floataa					)
      else:
         _lowerCAmelCase         =		torch.from_numpy(a__					).to(a__					)

      # interpolate timesteps
      _lowerCAmelCase         =		self.sigma_to_t(a__					).to(a__							,						dtype=timesteps.dtype					)
      _lowerCAmelCase         =		torch.stack((timesteps_interpol[1:-1, None], timesteps[1:, None])							,						dim=-1					).flatten()

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

      _lowerCAmelCase         =		None

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







   def 				A__    (self							,						lowerCamelCase					):




      '''simple docstring'''




      _lowerCAmelCase         =		sigma.log()

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

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

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

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

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







   @property
   def 				A__    (self					):




      '''simple docstring'''




      return self.sample is None







   def 				A__    (self							,						lowerCamelCase							,						lowerCamelCase							,						lowerCamelCase							,						lowerCamelCase = True							,						):




      '''simple docstring'''




      _lowerCAmelCase         =		self.index_for_timestep(a__					)

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

      if self.state_in_first_order:
         _lowerCAmelCase         =		self.sigmas[step_index]
         _lowerCAmelCase         =		self.sigmas_interpol[step_index + 1]
         _lowerCAmelCase         =		self.sigmas[step_index + 1]
      else:
         # 2nd order / KDPM2's method
         _lowerCAmelCase         =		self.sigmas[step_index - 1]
         _lowerCAmelCase         =		self.sigmas_interpol[step_index]
         _lowerCAmelCase         =		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
      _lowerCAmelCase         =		0
      _lowerCAmelCase         =		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":
         _lowerCAmelCase         =		sigma_hat if self.state_in_first_order else sigma_interpol
         _lowerCAmelCase         =		sample - sigma_input * model_output
      elif self.config.prediction_type == "v_prediction":
         _lowerCAmelCase         =		sigma_hat if self.state_in_first_order else sigma_interpol
         _lowerCAmelCase         =		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
         _lowerCAmelCase         =		(sample - pred_original_sample) / sigma_hat
         # 3. delta timestep
         _lowerCAmelCase         =		sigma_interpol - sigma_hat

         # store for 2nd order step
         _lowerCAmelCase         =		sample
      else:
         # DPM-Solver-2
         # 2. Convert to an ODE derivative for 2nd order
         _lowerCAmelCase         =		(sample - pred_original_sample) / sigma_interpol

         # 3. delta timestep
         _lowerCAmelCase         =		sigma_next - sigma_hat

         _lowerCAmelCase         =		self.sample
         _lowerCAmelCase         =		None

      _lowerCAmelCase         =		sample + derivative * dt

      if not return_dict:
         return (prev_sample,)

      return SchedulerOutput(prev_sample=a__					)







   def 				A__    (self							,						lowerCamelCase							,						lowerCamelCase							,						lowerCamelCase							,						):




      '''simple docstring'''




      _lowerCAmelCase         =		self.sigmas.to(device=original_samples.device							,						dtype=original_samples.dtype					)
      if original_samples.device.type == "mps" and torch.is_floating_point(a__					):
         # mps does not support float64
         _lowerCAmelCase         =		self.timesteps.to(original_samples.device							,						dtype=torch.floataa					)
         _lowerCAmelCase         =		timesteps.to(original_samples.device							,						dtype=torch.floataa					)
      else:
         _lowerCAmelCase         =		self.timesteps.to(original_samples.device					)
         _lowerCAmelCase         =		timesteps.to(original_samples.device					)

      _lowerCAmelCase         =		[self.index_for_timestep(a__							,						a__					) for t in timesteps]

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

      _lowerCAmelCase         =		original_samples + noise * sigma
      return noisy_samples







   def __len__(self					):




      '''simple docstring'''




      return self.config.num_train_timesteps






from __future__ import annotations




def  __UpperCAmelCase(   lowercase_			,     lowercase_ = None			,     lowercase_ = None			,     lowercase_ = False			,     ):
       _lowerCamelCase				:  Tuple						=		cipher_alphabet or [chr(lowercase_   ) for i in range(97			,     1_23   )]

       # If the argument is None or the user provided an empty dictionary
       if not frequencies_dict:
              # Frequencies of letters in the english language (how much they show up)
              _lowerCamelCase				:  Dict						=		{
                  '''a''': 0.0_8_4_9_7,
                  '''b''': 0.0_1_4_9_2,
                  '''c''': 0.0_2_2_0_2,
                  '''d''': 0.0_4_2_5_3,
                  '''e''': 0.1_1_1_6_2,
                  '''f''': 0.0_2_2_2_8,
                  '''g''': 0.0_2_0_1_5,
                  '''h''': 0.0_6_0_9_4,
                  '''i''': 0.0_7_5_4_6,
                  '''j''': 0.0_0_1_5_3,
                  '''k''': 0.0_1_2_9_2,
                  '''l''': 0.0_4_0_2_5,
                  '''m''': 0.0_2_4_0_6,
                  '''n''': 0.0_6_7_4_9,
                  '''o''': 0.0_7_5_0_7,
                  '''p''': 0.0_1_9_2_9,
                  '''q''': 0.0_0_0_9_5,
                  '''r''': 0.0_7_5_8_7,
                  '''s''': 0.0_6_3_2_7,
                  '''t''': 0.0_9_3_5_6,
                  '''u''': 0.0_2_7_5_8,
                  '''v''': 0.0_0_9_7_8,
                  '''w''': 0.0_2_5_6_0,
                  '''x''': 0.0_0_1_5_0,
                  '''y''': 0.0_1_9_9_4,
                  '''z''': 0.0_0_0_7_7,
              }
       else:
              # Custom frequencies dictionary
              _lowerCamelCase				:  Tuple						=		frequencies_dict

       if not case_sensitive:
              _lowerCamelCase				:  Optional[int]						=		ciphertext.lower()

       # Chi squared statistic values
       _lowerCamelCase				:  dict[int, tuple[float, str]]						=		{}

       # cycle through all of the shifts
       for shift in range(len(lowercase_   )   ):
              _lowerCamelCase				:  Any						=		''''''

              # decrypt the message with the shift
              for letter in ciphertext:
                     try:
                            # Try to index the letter in the alphabet
                            _lowerCamelCase				:  int						=		(alphabet_letters.index(letter.lower()   ) - shift) % len(
                                lowercase_   )
                            decrypted_with_shift += (
                                alphabet_letters[new_key].upper()
                                if case_sensitive and letter.isupper()
                                else alphabet_letters[new_key]
                            )
                     except ValueError:
                            # Append the character if it isn't in the alphabet
                            decrypted_with_shift += letter

              _lowerCamelCase				:  Optional[Any]						=		0.0

              # Loop through each letter in the decoded message with the shift
              for letter in decrypted_with_shift:
                     if case_sensitive:
                            _lowerCamelCase				:  Any						=		letter.lower()
                            if letter in frequencies:
                                   # Get the amount of times the letter occurs in the message
                                   _lowerCamelCase				:  List[str]						=		decrypted_with_shift.lower().count(lowercase_   )

                                   # Get the excepcted amount of times the letter should appear based
                                   # on letter frequencies
                                   _lowerCamelCase				:  Optional[Any]						=		frequencies[letter] * occurrences

                                   # Complete the chi squared statistic formula
                                   _lowerCamelCase				:  int						=		((occurrences - expected) ** 2) / expected

                                   # Add the margin of error to the total chi squared statistic
                                   chi_squared_statistic += chi_letter_value
                     else:
                            if letter.lower() in frequencies:
                                   # Get the amount of times the letter occurs in the message
                                   _lowerCamelCase				:  Union[str, Any]						=		decrypted_with_shift.count(lowercase_   )

                                   # Get the excepcted amount of times the letter should appear based
                                   # on letter frequencies
                                   _lowerCamelCase				:  List[str]						=		frequencies[letter] * occurrences

                                   # Complete the chi squared statistic formula
                                   _lowerCamelCase				:  str						=		((occurrences - expected) ** 2) / expected

                                   # Add the margin of error to the total chi squared statistic
                                   chi_squared_statistic += chi_letter_value

        # Add the data to the chi_squared_statistic_values dictionary
              _lowerCamelCase				:  Tuple						=		(
                  chi_squared_statistic,
                  decrypted_with_shift,
              )

       # Get the most likely cipher by finding the cipher with the smallest chi squared
       # statistic
       def chi_squared_statistic_values_sorting_key(lowercase_   ) -> tuple[float, str]:
              return chi_squared_statistic_values[key]

       _lowerCamelCase				:  int						=		min(
           lowercase_			,     key=lowercase_			,     )

       # Get all the data from the most likely cipher (key, decoded message)
       (
           (
           _lowerCamelCase
       ),	(
           _lowerCamelCase
       ),	
       )				:  Optional[int]						=		chi_squared_statistic_values[most_likely_cipher]

       # Return the data on the most likely shift
       return (
           most_likely_cipher,
           most_likely_cipher_chi_squared_value,
           decoded_most_likely_cipher,
       )

