
import math
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, logging, randn_tensor
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin


__lowerCamelCase								=					logging.get_logger(__name__)  # pylint: disable=invalid-name
@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerDiscrete
class    _UpperCamelCase(   SCREAMING_SNAKE_CASE				):
						__A:						torch.FloatTensor
						__A:						Optional[torch.FloatTensor]				   =      None







def 		lowerCAmelCase_     (     _SCREAMING_SNAKE_CASE      ,	_SCREAMING_SNAKE_CASE=0.999      ,	_SCREAMING_SNAKE_CASE="cosine"      ,	)   ->      Tuple:

							"""simple docstring"""






							if alpha_transform_type == "cosine":

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

							elif alpha_transform_type == "exp":

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

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

							_UpperCAmelCase  :			Dict	       =		[]
							for i in range(_SCREAMING_SNAKE_CASE  ):
														_UpperCAmelCase  :			Dict	       =		i / num_diffusion_timesteps
														_UpperCAmelCase  :			Optional[Any]	       =		(i + 1) / num_diffusion_timesteps
														betas.append(min(1 - alpha_bar_fn(_SCREAMING_SNAKE_CASE  ) / alpha_bar_fn(_SCREAMING_SNAKE_CASE  )      ,	_SCREAMING_SNAKE_CASE  )  )
							return torch.tensor(_SCREAMING_SNAKE_CASE      ,	dtype=torch.floataa  )


class    _UpperCamelCase(   SCREAMING_SNAKE_CASE		,						SCREAMING_SNAKE_CASE				):
						__A:						Dict				   =      [e.name for e in KarrasDiffusionSchedulers]
						__A:						str				   =      1

						@register_to_config
						def __init__(					self		:			Dict	,						_lowerCamelCase		:			int = 10_00	,						_lowerCamelCase		:			float = 0.00_01	,						_lowerCamelCase		:			float = 0.02	,						_lowerCamelCase		:			str = "linear"	,						_lowerCamelCase		:			Optional[Union[np.ndarray, List[float]]] = None	,						_lowerCamelCase		:			str = "epsilon"	,						_lowerCamelCase		:			str = "linear"	,						_lowerCamelCase		:			Optional[bool] = False	,						_lowerCamelCase		:			str = "linspace"	,						_lowerCamelCase		:			int = 0	,						):
													if trained_betas is not None:
																				_UpperCAmelCase  :			str	       =		torch.tensor(_lowerCamelCase	,						dtype=torch.floataa			)
													elif beta_schedule == "linear":
																				_UpperCAmelCase  :			str	       =		torch.linspace(_lowerCamelCase	,						_lowerCamelCase	,						_lowerCamelCase	,						dtype=torch.floataa			)
													elif beta_schedule == "scaled_linear":
																				# this schedule is very specific to the latent diffusion model.
																				_UpperCAmelCase  :			Optional[int]	       =		(
																				    torch.linspace(beta_start**0.5	,						beta_end**0.5	,						_lowerCamelCase	,						dtype=torch.floataa			) ** 2
																				)
													elif beta_schedule == "squaredcos_cap_v2":
																				# Glide cosine schedule
																				_UpperCAmelCase  :			Optional[int]	       =		betas_for_alpha_bar(_lowerCamelCase			)
													else:
																				raise NotImplementedError(f"""{beta_schedule} does is not implemented for {self.__class__}"""			)

													_UpperCAmelCase  :			str	       =		1.0 - self.betas
													_UpperCAmelCase  :			Any	       =		torch.cumprod(self.alphas	,						dim=0			)

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

													# setable values
													_UpperCAmelCase  :			Tuple	       =		None
													_UpperCAmelCase  :			Optional[int]	       =		np.linspace(0	,						num_train_timesteps - 1	,						_lowerCamelCase	,						dtype=_lowerCamelCase			)[::-1].copy()
													_UpperCAmelCase  :			int	       =		torch.from_numpy(_lowerCamelCase			)
													_UpperCAmelCase  :			Optional[int]	       =		False
													_UpperCAmelCase  :			Dict	       =		use_karras_sigmas

						@property
						def 						a__ (					self		:			List[str]			):
													# 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		:			str	,						_lowerCamelCase		:			torch.FloatTensor	,						_lowerCamelCase		:			Union[float, torch.FloatTensor]			):
													if isinstance(_lowerCamelCase	,						torch.Tensor			):
																				_UpperCAmelCase  :			int	       =		timestep.to(self.timesteps.device			)
													_UpperCAmelCase  :			Union[str, Any]	       =		(self.timesteps == timestep).nonzero().item()
													_UpperCAmelCase  :			str	       =		self.sigmas[step_index]

													_UpperCAmelCase  :			Dict	       =		sample / ((sigma**2 + 1) ** 0.5)

													_UpperCAmelCase  :			Any	       =		True
													return sample

						def 						a__ (					self		:			Optional[Any]	,						_lowerCamelCase		:			int	,						_lowerCamelCase		:			Union[str, torch.device] = None			):
													_UpperCAmelCase  :			Any	       =		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":
																				_UpperCAmelCase  :			int	       =		np.linspace(0	,						self.config.num_train_timesteps - 1	,						_lowerCamelCase	,						dtype=_lowerCamelCase			)[
																				    ::-1
																				].copy()
													elif self.config.timestep_spacing == "leading":
																				_UpperCAmelCase  :			str	       =		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
																				_UpperCAmelCase  :			List[str]	       =		(np.arange(0	,						_lowerCamelCase			) * step_ratio).round()[::-1].copy().astype(_lowerCamelCase			)
																				timesteps += self.config.steps_offset
													elif self.config.timestep_spacing == "trailing":
																				_UpperCAmelCase  :			int	       =		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
																				_UpperCAmelCase  :			Optional[int]	       =		(np.arange(self.config.num_train_timesteps	,						0	,						-step_ratio			)).round().copy().astype(_lowerCamelCase			)
																				timesteps -= 1
													else:
																				raise ValueError(
																				    f"""{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'."""			)

													_UpperCAmelCase  :			Optional[Any]	       =		np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5			)
													_UpperCAmelCase  :			List[Any]	       =		np.log(_lowerCamelCase			)

													if self.config.interpolation_type == "linear":
																				_UpperCAmelCase  :			Any	       =		np.interp(_lowerCamelCase	,						np.arange(0	,						len(_lowerCamelCase			)			)	,						_lowerCamelCase			)
													elif self.config.interpolation_type == "log_linear":
																				_UpperCAmelCase  :			str	       =		torch.linspace(np.log(sigmas[-1]			)	,						np.log(sigmas[0]			)	,						num_inference_steps + 1			).exp()
													else:
																				raise ValueError(
																				    f"""{self.config.interpolation_type} is not implemented. Please specify interpolation_type to either"""
																				    " 'linear' or 'log_linear'"			)

													if self.use_karras_sigmas:
																				_UpperCAmelCase  :			Tuple	       =		self._convert_to_karras(in_sigmas=_lowerCamelCase	,						num_inference_steps=self.num_inference_steps			)
																				_UpperCAmelCase  :			List[Any]	       =		np.array([self._sigma_to_t(_lowerCamelCase	,						_lowerCamelCase			) for sigma in sigmas]			)

													_UpperCAmelCase  :			str	       =		np.concatenate([sigmas, [0.0]]			).astype(np.floataa			)
													_UpperCAmelCase  :			Optional[int]	       =		torch.from_numpy(_lowerCamelCase			).to(device=_lowerCamelCase			)
													if str(_lowerCamelCase			).startswith("mps"			):
																				# mps does not support float64
																				_UpperCAmelCase  :			List[str]	       =		torch.from_numpy(_lowerCamelCase			).to(_lowerCamelCase	,						dtype=torch.floataa			)
													else:
																				_UpperCAmelCase  :			str	       =		torch.from_numpy(_lowerCamelCase			).to(device=_lowerCamelCase			)

						def 						a__ (					self		:			str	,						_lowerCamelCase		:			Optional[int]	,						_lowerCamelCase		:			Tuple			):
													# get log sigma
													_UpperCAmelCase  :			Tuple	       =		np.log(_lowerCamelCase			)

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

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

													_UpperCAmelCase  :			Any	       =		log_sigmas[low_idx]
													_UpperCAmelCase  :			List[Any]	       =		log_sigmas[high_idx]

													# interpolate sigmas
													_UpperCAmelCase  :			Optional[Any]	       =		(low - log_sigma) / (low - high)
													_UpperCAmelCase  :			Optional[int]	       =		np.clip(_lowerCamelCase	,						0	,						1			)

													# transform interpolation to time range
													_UpperCAmelCase  :			Optional[Any]	       =		(1 - w) * low_idx + w * high_idx
													_UpperCAmelCase  :			Optional[int]	       =		t.reshape(sigma.shape			)
													return t

						def 						a__ (					self		:			Tuple	,						_lowerCamelCase		:			torch.FloatTensor	,						_lowerCamelCase		:			int			):
													_UpperCAmelCase  :			float	       =		in_sigmas[-1].item()
													_UpperCAmelCase  :			float	       =		in_sigmas[0].item()

													_UpperCAmelCase  :			Tuple	       =		7.0  # 7.0 is the value used in the paper
													_UpperCAmelCase  :			Any	       =		np.linspace(0	,						1	,						_lowerCamelCase			)
													_UpperCAmelCase  :			int	       =		sigma_min ** (1 / rho)
													_UpperCAmelCase  :			List[Any]	       =		sigma_max ** (1 / rho)
													_UpperCAmelCase  :			List[str]	       =		(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
													return sigmas

						def 						a__ (					self		:			str	,						_lowerCamelCase		:			torch.FloatTensor	,						_lowerCamelCase		:			Union[float, torch.FloatTensor]	,						_lowerCamelCase		:			torch.FloatTensor	,						_lowerCamelCase		:			float = 0.0	,						_lowerCamelCase		:			float = 0.0	,						_lowerCamelCase		:			float = float("inf"			)	,						_lowerCamelCase		:			float = 1.0	,						_lowerCamelCase		:			Optional[torch.Generator] = None	,						_lowerCamelCase		:			bool = True	,						):

													if (
													    isinstance(_lowerCamelCase	,						_lowerCamelCase			)
													    or isinstance(_lowerCamelCase	,						torch.IntTensor			)
													    or isinstance(_lowerCamelCase	,						torch.LongTensor			)
													):
																				raise ValueError(
																				    (
																				        "Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to"
																				        " `EulerDiscreteScheduler.step()` is not supported. Make sure to pass"
																				        " one of the `scheduler.timesteps` as a timestep."
																				    )	,						)

													if not self.is_scale_input_called:
																				logger.warning(
																				    "The `scale_model_input` function should be called before `step` to ensure correct denoising. "
																				    "See `StableDiffusionPipeline` for a usage example."			)

													if isinstance(_lowerCamelCase	,						torch.Tensor			):
																				_UpperCAmelCase  :			Dict	       =		timestep.to(self.timesteps.device			)

													_UpperCAmelCase  :			Any	       =		(self.timesteps == timestep).nonzero().item()
													_UpperCAmelCase  :			Any	       =		self.sigmas[step_index]

													_UpperCAmelCase  :			str	       =		min(s_churn / (len(self.sigmas			) - 1)	,						2**0.5 - 1			) if s_tmin <= sigma <= s_tmax else 0.0

													_UpperCAmelCase  :			Optional[Any]	       =		randn_tensor(
													    model_output.shape	,						dtype=model_output.dtype	,						device=model_output.device	,						generator=_lowerCamelCase			)

													_UpperCAmelCase  :			Union[str, Any]	       =		noise * s_noise
													_UpperCAmelCase  :			Union[str, Any]	       =		sigma * (gamma + 1)

													if gamma > 0:
																				_UpperCAmelCase  :			List[str]	       =		sample + eps * (sigma_hat**2 - sigma**2) ** 0.5

													# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
													# NOTE: "original_sample" should not be an expected prediction_type but is left in for
													# backwards compatibility
													if self.config.prediction_type == "original_sample" or self.config.prediction_type == "sample":
																				_UpperCAmelCase  :			Optional[int]	       =		model_output
													elif self.config.prediction_type == "epsilon":
																				_UpperCAmelCase  :			Optional[int]	       =		sample - sigma_hat * model_output
													elif self.config.prediction_type == "v_prediction":
																				# * c_out + input * c_skip
																				_UpperCAmelCase  :			Union[str, Any]	       =		model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
													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
													_UpperCAmelCase  :			Union[str, Any]	       =		(sample - pred_original_sample) / sigma_hat

													_UpperCAmelCase  :			Union[str, Any]	       =		self.sigmas[step_index + 1] - sigma_hat

													_UpperCAmelCase  :			str	       =		sample + derivative * dt

													if not return_dict:
																				return (prev_sample,)

													return EulerDiscreteSchedulerOutput(prev_sample=_lowerCamelCase	,						pred_original_sample=_lowerCamelCase			)

						def 						a__ (					self		:			Any	,						_lowerCamelCase		:			torch.FloatTensor	,						_lowerCamelCase		:			torch.FloatTensor	,						_lowerCamelCase		:			torch.FloatTensor	,						):
													# Make sure sigmas and timesteps have the same device and dtype as original_samples
													_UpperCAmelCase  :			Union[str, Any]	       =		self.sigmas.to(device=original_samples.device	,						dtype=original_samples.dtype			)
													if original_samples.device.type == "mps" and torch.is_floating_point(_lowerCamelCase			):
																				# mps does not support float64
																				_UpperCAmelCase  :			Tuple	       =		self.timesteps.to(original_samples.device	,						dtype=torch.floataa			)
																				_UpperCAmelCase  :			List[Any]	       =		timesteps.to(original_samples.device	,						dtype=torch.floataa			)
													else:
																				_UpperCAmelCase  :			Union[str, Any]	       =		self.timesteps.to(original_samples.device			)
																				_UpperCAmelCase  :			List[str]	       =		timesteps.to(original_samples.device			)

													_UpperCAmelCase  :			Union[str, Any]	       =		[(schedule_timesteps == t).nonzero().item() for t in timesteps]

													_UpperCAmelCase  :			int	       =		sigmas[step_indices].flatten()
													while len(sigma.shape			) < len(original_samples.shape			):
																				_UpperCAmelCase  :			List[str]	       =		sigma.unsqueeze(-1			)

													_UpperCAmelCase  :			Dict	       =		original_samples + noise * sigma
													return noisy_samples






						def __len__(					self		:			Optional[int]			):
													return self.config.num_train_timesteps






def 		lowerCAmelCase_     (     _SCREAMING_SNAKE_CASE      ,	_SCREAMING_SNAKE_CASE      ,	_SCREAMING_SNAKE_CASE  )   ->      Dict:

							"""simple docstring"""






							if power < 0:
														return -1
							base %= mod
							_UpperCAmelCase  :			Optional[Any]	       =		1

							while power > 0:
														if power & 1:
																					_UpperCAmelCase  :			Optional[Any]	       =		(result * base) % mod
														_UpperCAmelCase  :			List[str]	       =		power >> 1
														_UpperCAmelCase  :			Optional[int]	       =		(base * base) % mod

							return result




def 		lowerCAmelCase_     (     )   ->      List[str]:

							"""simple docstring"""






							print(modular_exponential(3      ,	2_0_0      ,	1_3  )  )


if __name__ == "__main__":
				import doctest

				doctest.testmod()

				main()




