


"""simple docstring"""




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  __snake_case      (lowerCamelCase     ):
							__a				   =					42
							__a				   =					None





def 			a_   (  lowercase__   :List[Any], lowercase__   :str=0.999, lowercase__   :Tuple="cosine", ):






			if alpha_transform_type == "cosine":

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

			elif alpha_transform_type == "exp":

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

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

			__lowerCamelCase        =			[]
			for i in range(_UpperCAmelCase    ):
						__lowerCamelCase        =			i / num_diffusion_timesteps
						__lowerCamelCase        =			(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  __snake_case      (lowerCamelCase ,		lowerCamelCase     ):
							__a				   =					[e.name for e in KarrasDiffusionSchedulers]
							__a				   =					1




							@register_to_config
							def __init__(    self:						List[str]    ,       A_:						int = 10_00    ,       A_:						float = 0.0_001    ,       A_:						float = 0.02    ,       A_:						str = "linear"    ,       A_:						Optional[Union[np.ndarray, List[float]]] = None    ,       A_:						Optional[bool] = False    ,       A_:						str = "epsilon"    ,       A_:						str = "linspace"    ,       A_:						int = 0    ,       ):
										if trained_betas is not None:
													__lowerCamelCase        =			torch.tensor(UpperCAmelCase_    ,       dtype=torch.floataa      )
										elif beta_schedule == "linear":
													__lowerCamelCase        =			torch.linspace(UpperCAmelCase_    ,       UpperCAmelCase_    ,       UpperCAmelCase_    ,       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    ,       UpperCAmelCase_    ,       dtype=torch.floataa      ) ** 2
													)
										elif beta_schedule == "squaredcos_cap_v2":
													# Glide cosine schedule
													__lowerCamelCase        =			betas_for_alpha_bar(UpperCAmelCase_      )
										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      )

										__lowerCamelCase        =			np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5      )
										__lowerCamelCase        =			np.concatenate([sigmas[::-1], [0.0]]      ).astype(np.floataa      )
										__lowerCamelCase        =			torch.from_numpy(UpperCAmelCase_      )

										# setable values
										__lowerCamelCase        =			None
										__lowerCamelCase        =			use_karras_sigmas
										self.set_timesteps(UpperCAmelCase_    ,       UpperCAmelCase_      )
										__lowerCamelCase        =			[]
										__lowerCamelCase        =			False




							@property
							def      __a      (    self:						Dict      ):
										# 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      __a      (    self:						Any    ,       A_:						torch.FloatTensor    ,       A_:						Union[float, torch.FloatTensor]      ):
										if isinstance(UpperCAmelCase_    ,       torch.Tensor      ):
													__lowerCamelCase        =			timestep.to(self.timesteps.device      )
										__lowerCamelCase        =			(self.timesteps == timestep).nonzero().item()
										__lowerCamelCase        =			self.sigmas[step_index]
										__lowerCamelCase        =			sample / ((sigma**2 + 1) ** 0.5)
										__lowerCamelCase        =			True
										return sample




							def      __a      (    self:						Any    ,       A_:						Any    ,       A_:						Tuple    ,       A_:						Optional[Any]      ):

										def lms_derivative(A_:						int      ):
													__lowerCamelCase        =			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

										__lowerCamelCase        =			integrate.quad(UpperCAmelCase_    ,       self.sigmas[t]    ,       self.sigmas[t + 1]    ,       epsrel=1E-4      )[0]

										return integrated_coeff




							def      __a      (    self:						int    ,       A_:						int    ,       A_:						Union[str, torch.device] = None      ):
										__lowerCamelCase        =			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":
													__lowerCamelCase        =			np.linspace(0    ,       self.config.num_train_timesteps - 1    ,       UpperCAmelCase_    ,       dtype=UpperCAmelCase_      )[
													    ::-1
													].copy()
										elif self.config.timestep_spacing == "leading":
													__lowerCamelCase        =			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
													__lowerCamelCase        =			(np.arange(0    ,       UpperCAmelCase_      ) * step_ratio).round()[::-1].copy().astype(UpperCAmelCase_      )
													timesteps += self.config.steps_offset
										elif self.config.timestep_spacing == "trailing":
													__lowerCamelCase        =			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
													__lowerCamelCase        =			(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\'.'      )

										__lowerCamelCase        =			np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5      )
										__lowerCamelCase        =			np.log(UpperCAmelCase_      )
										__lowerCamelCase        =			np.interp(UpperCAmelCase_    ,       np.arange(0    ,       len(UpperCAmelCase_      )      )    ,       UpperCAmelCase_      )

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

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

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

										__lowerCamelCase        =			[]




							def      __a      (    self:						str    ,       A_:						Optional[Any]    ,       A_:						List[str]      ):
										# get log sigma
										__lowerCamelCase        =			np.log(UpperCAmelCase_      )

										# get distribution
										__lowerCamelCase        =			log_sigma - log_sigmas[:, np.newaxis]

										# get sigmas range
										__lowerCamelCase        =			np.cumsum((dists >= 0)    ,       axis=0      ).argmax(axis=0      ).clip(max=log_sigmas.shape[0] - 2      )
										__lowerCamelCase        =			low_idx + 1

										__lowerCamelCase        =			log_sigmas[low_idx]
										__lowerCamelCase        =			log_sigmas[high_idx]

										# interpolate sigmas
										__lowerCamelCase        =			(low - log_sigma) / (low - high)
										__lowerCamelCase        =			np.clip(UpperCAmelCase_    ,       0    ,       1      )

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




							def      __a      (    self:						Any    ,       A_:						torch.FloatTensor      ):
										__lowerCamelCase        =			in_sigmas[-1].item()
										__lowerCamelCase        =			in_sigmas[0].item()

										__lowerCamelCase        =			7.0  # 7.0 is the value used in the paper
										__lowerCamelCase        =			np.linspace(0    ,       1    ,       self.num_inference_steps      )
										__lowerCamelCase        =			sigma_min ** (1 / rho)
										__lowerCamelCase        =			sigma_max ** (1 / rho)
										__lowerCamelCase        =			(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
										return sigmas




							def      __a      (    self:						Optional[int]    ,       A_:						torch.FloatTensor    ,       A_:						Union[float, torch.FloatTensor]    ,       A_:						torch.FloatTensor    ,       A_:						int = 4    ,       A_:						bool = True    ,       ):
										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      ):
													__lowerCamelCase        =			timestep.to(self.timesteps.device      )
										__lowerCamelCase        =			(self.timesteps == timestep).nonzero().item()
										__lowerCamelCase        =			self.sigmas[step_index]

										# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
										if self.config.prediction_type == "epsilon":
													__lowerCamelCase        =			sample - sigma * model_output
										elif self.config.prediction_type == "v_prediction":
													# * c_out + input * c_skip
													__lowerCamelCase        =			model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
										elif self.config.prediction_type == "sample":
													__lowerCamelCase        =			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
										__lowerCamelCase        =			(sample - pred_original_sample) / sigma
										self.derivatives.append(UpperCAmelCase_      )
										if len(self.derivatives      ) > order:
													self.derivatives.pop(0      )

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

										# 4. Compute previous sample based on the derivatives path
										__lowerCamelCase        =			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      __a      (    self:						Optional[int]    ,       A_:						torch.FloatTensor    ,       A_:						torch.FloatTensor    ,       A_:						torch.FloatTensor    ,       ):
										# Make sure sigmas and timesteps have the same device and dtype as original_samples
										__lowerCamelCase        =			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
													__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        =			[(schedule_timesteps == t).nonzero().item() 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:						Dict      ):
										return self.config.num_train_timesteps








"""simple docstring"""




def 			a_   (  lowercase__   :str, lowercase__   :int = 13    ):
			__lowerCamelCase        =			""""""
			for c in s:
						if "A" <= c <= "Z":
									out += chr(ord("""A"""    ) + (ord(lowercase__    ) - ord("""A"""    ) + n) % 26    )
						elif "a" <= c <= "z":
									out += chr(ord("""a"""    ) + (ord(lowercase__    ) - ord("""a"""    ) + n) % 26    )
						else:
									out += c
			return out





def 			a_   (  ):
			__lowerCamelCase        =			input("""Enter message: """    )

			__lowerCamelCase        =			dencrypt(lowercase__, 13    )
			print("""Encryption:""", lowercase__    )

			__lowerCamelCase        =			dencrypt(lowercase__, 13    )
			print("""Decryption: """, lowercase__    )


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					main()




