


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 					lowerCAmelCase_     (    UpperCAmelCase  ):
       __UpperCAmelCase				=42
       __UpperCAmelCase				=None






def 				lowerCamelCase_   (   __UpperCamelCase				:					Optional[int]       ,						__UpperCamelCase				:					Tuple=0.9_99       ,						__UpperCamelCase				:					Any="cosine"       ,						)				->  str:







     """simple docstring"""
     if alpha_transform_type == "cosine":

          def alpha_bar_fn(__UpperCamelCase				:					Optional[int]		):
               return math.cos((t + 0.0_08) / 1.0_08 * math.pi / 2		) ** 2

     elif alpha_transform_type == "exp":

          def alpha_bar_fn(__UpperCamelCase				:					Any		):
               return math.exp(t * -12.0		)

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

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






class 					lowerCAmelCase_     (    UpperCAmelCase			,       UpperCAmelCase  ):
       __UpperCAmelCase				=[e.name for e in KarrasDiffusionSchedulers]
       __UpperCAmelCase				=1






       @register_to_config
       def __init__(   self ,    _UpperCamelCase = 1000 ,    _UpperCamelCase = 0.0001 ,    _UpperCamelCase = 0.02 ,    _UpperCamelCase = "linear" ,    _UpperCamelCase = None ,    _UpperCamelCase = False ,    _UpperCamelCase = "epsilon" ,    _UpperCamelCase = "linspace" ,    _UpperCamelCase = 0 ,    )->			Tuple:
            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      )

            _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(_UpperCamelCase      )

            # setable values
            _A				=       None
            _A				=       use_karras_sigmas
            self.set_timesteps(_UpperCamelCase ,    _UpperCamelCase      )
            _A				=       []
            _A				=       False






       @property
       def      UpperCamelCase	(   self      )->			Union[str, Any]:
            # 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 ,    _UpperCamelCase ,    _UpperCamelCase      )->			torch.FloatTensor:
            if isinstance(_UpperCamelCase ,    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 ,    _UpperCamelCase ,    _UpperCamelCase ,    _UpperCamelCase      )->			str:

            def lms_derivative(_UpperCamelCase      ):
                 _A				=       1.0
                 for k in range(_UpperCamelCase      ):
                      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(_UpperCamelCase ,    self.sigmas[t] ,    self.sigmas[t + 1] ,    epsrel=1e-4      )[0]

            return integrated_coeff






       def      UpperCamelCase	(   self ,    _UpperCamelCase ,    _UpperCamelCase = None      )->			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 ,    _UpperCamelCase ,    dtype=_UpperCamelCase      )[
                     ::-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 ,    _UpperCamelCase      ) * step_ratio).round()[::-1].copy().astype(_UpperCamelCase      )
                 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(_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				=       np.log(_UpperCamelCase      )
            _A				=       np.interp(_UpperCamelCase ,    np.arange(0 ,    len(_UpperCamelCase      )      ) ,    _UpperCamelCase      )

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

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

            _A				=       torch.from_numpy(_UpperCamelCase      ).to(device=_UpperCamelCase      )
            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(device=_UpperCamelCase      )

            _A				=       []






       def      UpperCamelCase	(   self ,    _UpperCamelCase ,    _UpperCamelCase      )->			List[Any]:
            # get log sigma
            _A				=       np.log(_UpperCamelCase      )

            # 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(_UpperCamelCase ,    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 ,    _UpperCamelCase      )->			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 ,    _UpperCamelCase ,    _UpperCamelCase ,    _UpperCamelCase ,    _UpperCamelCase = 4 ,    _UpperCamelCase = 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(_UpperCamelCase ,    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(_UpperCamelCase      )
            if len(self.derivatives      ) > order:
                 self.derivatives.pop(0      )

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

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

            if not return_dict:
                 return (prev_sample,)

            return LMSDiscreteSchedulerOutput(prev_sample=_UpperCamelCase ,    pred_original_sample=_UpperCamelCase      )






       def      UpperCamelCase	(   self ,    _UpperCamelCase ,    _UpperCamelCase ,    _UpperCamelCase ,    )->			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(_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				=       [(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[Any]:
            return self.config.num_train_timesteps









'''simple docstring'''
from __future__ import annotations

def 				lowerCamelCase_   (   __UpperCamelCase				:					str       ,						__UpperCamelCase				:					dict[str, str]		)				->  str:







     """simple docstring"""
     _A		,							_A		,							_A				=       '', '', ''
     _A				=       []

     for character in message_part:
          tmp.append(character_to_number[character]		)

     for each in tmp:
          one += each[0]
          two += each[1]
          three += each[2]

     return one + two + three

def 				lowerCamelCase_   (   __UpperCamelCase				:					str       ,						__UpperCamelCase				:					dict[str, str]		)				->  tuple[str, str, str]:







     """simple docstring"""
     _A		,							_A				=       '', ''
     _A				=       []

     for character in message_part:
          this_part += character_to_number[character]

     for digit in this_part:
          tmp += digit
          if len(__UpperCamelCase		) == len(__UpperCamelCase		):
               result.append(__UpperCamelCase		)
               _A				=       ''

     return result[0], result[1], result[2]

def 				lowerCamelCase_   (   __UpperCamelCase				:					str       ,						__UpperCamelCase				:					str		)				->  tuple[str, str, dict[str, str], dict[str, str]]:







     """simple docstring"""
     # Validate message and alphabet, set to upper and remove spaces
     _A				=       alphabet.replace(' '       ,						''		).upper()
     _A				=       message.replace(' '       ,						''		).upper()

     # Check length and characters
     if len(__UpperCamelCase		) != 2_7:
          raise KeyError('Length of alphabet has to be 27.'		)
     for each in message:
          if each not in alphabet:
               raise ValueError('Each message character has to be included in alphabet!'		)

    # Generate dictionares
     _A				=       (
         '111',
         '112',
         '113',
         '121',
         '122',
         '123',
         '131',
         '132',
         '133',
         '211',
         '212',
         '213',
         '221',
         '222',
         '223',
         '231',
         '232',
         '233',
         '311',
         '312',
         '313',
         '321',
         '322',
         '323',
         '331',
         '332',
         '333',
     )
     _A				=       {}
     _A				=       {}
     for letter, number in zip(__UpperCamelCase       ,						__UpperCamelCase		):
          _A				=       number
          _A				=       letter

     return message, alphabet, character_to_number, number_to_character

def 				lowerCamelCase_   (   __UpperCamelCase				:					str       ,						__UpperCamelCase				:					str = "ABCDEFGHIJKLMNOPQRSTUVWXYZ."       ,						__UpperCamelCase				:					int = 5		)				->  str:







     """simple docstring"""
     _A		,							_A		,							_A		,							_A				=       __prepare(
         __UpperCamelCase       ,						__UpperCamelCase		)
     _A		,							_A				=       '', ''

     for i in range(0       ,						len(__UpperCamelCase		) + 1       ,						__UpperCamelCase		):
          encrypted_numeric += __encrypt_part(
              message[i : i + period]       ,						__UpperCamelCase		)

     for i in range(0       ,						len(__UpperCamelCase		)       ,						3		):
          encrypted += number_to_character[encrypted_numeric[i : i + 3]]

     return encrypted

def 				lowerCamelCase_   (   __UpperCamelCase				:					str       ,						__UpperCamelCase				:					str = "ABCDEFGHIJKLMNOPQRSTUVWXYZ."       ,						__UpperCamelCase				:					int = 5		)				->  str:







     """simple docstring"""
     _A		,							_A		,							_A		,							_A				=       __prepare(
         __UpperCamelCase       ,						__UpperCamelCase		)
     _A				=       []
     _A				=       ''

     for i in range(0       ,						len(__UpperCamelCase		) + 1       ,						__UpperCamelCase		):
          _A		,							_A		,							_A				=       __decrypt_part(message[i : i + period]       ,						__UpperCamelCase		)

          for j in range(0       ,						len(__UpperCamelCase		)		):
               decrypted_numeric.append(a[j] + b[j] + c[j]		)

     for each in decrypted_numeric:
          decrypted += number_to_character[each]

     return decrypted


if __name__ == "__main__":
    lowerCAmelCase  =				"""DEFEND THE EAST WALL OF THE CASTLE."""
    lowerCAmelCase  =				encrypt_message(msg, """EPSDUCVWYM.ZLKXNBTFGORIJHAQ""")
    lowerCAmelCase  =				decrypt_message(encrypted, """EPSDUCVWYM.ZLKXNBTFGORIJHAQ""")
    print(F'Encrypted: {encrypted}\nDecrypted: {decrypted}')





