


'''simple docstring'''
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


__SCREAMING_SNAKE_CASE				:							Any		       =		logging.get_logger(__name__)  # pylint: disable=invalid-name






@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerDiscrete
class 				__lowerCAmelCase      (      lowercase	):

						"""simple docstring"""






						_UpperCAmelCase		:					torch.FloatTensor
						_UpperCAmelCase		:					Optional[torch.FloatTensor]      	=None







def 			a_							(  UpperCamelCase_	,     UpperCamelCase_=0.999	,     UpperCamelCase_="cosine"	,     ):
							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 * -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      (      lowercase							, lowercase	):

						"""simple docstring"""






						_UpperCAmelCase		:					Any      	=[e.name for e in KarrasDiffusionSchedulers]
						_UpperCAmelCase		:					Tuple      	=1






						@register_to_config
						def __init__(     self       :			List[str]   ,     lowerCAmelCase       :			int = 10_00   ,     lowerCAmelCase       :			float = 0.0_0_0_1   ,     lowerCAmelCase       :			float = 0.0_2   ,     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:
																				A_ 						=		torch.tensor(lowerCAmelCase   ,     dtype=torch.floataa  )
													elif beta_schedule == "linear":
																				A_ 						=		torch.linspace(lowerCAmelCase   ,     lowerCAmelCase   ,     lowerCAmelCase   ,     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   ,     lowerCAmelCase   ,     dtype=torch.floataa  ) ** 2
																				)
													elif beta_schedule == "squaredcos_cap_v2":
																				# Glide cosine schedule
																				A_ 						=		betas_for_alpha_bar(lowerCAmelCase  )
													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(lowerCAmelCase  )

													# setable values
													A_ 						=		None
													A_ 						=		np.linspace(0   ,     num_train_timesteps - 1   ,     lowerCAmelCase   ,     dtype=lowerCAmelCase  )[::-1].copy()
													A_ 						=		torch.from_numpy(lowerCAmelCase  )
													A_ 						=		False
													A_ 						=		use_karras_sigmas






						@property
						def 							_UpperCAmelCase					(     self       :			Tuple  ):
													# 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       :			str   ,     lowerCAmelCase       :			torch.FloatTensor   ,     lowerCAmelCase       :			Union[float, torch.FloatTensor]  ):
													if isinstance(lowerCAmelCase   ,     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       :			Dict   ,     lowerCAmelCase       :			int   ,     lowerCAmelCase       :			Union[str, torch.device] = None  ):
													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   ,     lowerCAmelCase   ,     dtype=lowerCAmelCase  )[
																				    ::-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   ,     lowerCAmelCase  ) * step_ratio).round()[::-1].copy().astype(lowerCAmelCase  )
																				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(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'."  )

													A_ 						=		np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5  )
													A_ 						=		np.log(lowerCAmelCase  )

													if self.config.interpolation_type == "linear":
																				A_ 						=		np.interp(lowerCAmelCase   ,     np.arange(0   ,     len(lowerCAmelCase  )  )   ,     lowerCAmelCase  )
													elif self.config.interpolation_type == "log_linear":
																				A_ 						=		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:
																				A_ 						=		self._convert_to_karras(in_sigmas=lowerCAmelCase   ,     num_inference_steps=self.num_inference_steps  )
																				A_ 						=		np.array([self._sigma_to_t(lowerCAmelCase   ,     lowerCAmelCase  ) for sigma in sigmas]  )

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






						def 							_UpperCAmelCase					(     self       :			str   ,     lowerCAmelCase       :			Optional[int]   ,     lowerCAmelCase       :			List[Any]  ):
													# get log sigma
													A_ 						=		np.log(lowerCAmelCase  )

													# 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(lowerCAmelCase   ,     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       :			List[Any]   ,     lowerCAmelCase       :			torch.FloatTensor   ,     lowerCAmelCase       :			List[Any]  ):
													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   ,     lowerCAmelCase  )
													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       :			Dict   ,     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  ):
																				A_ 						=		timestep.to(self.timesteps.device  )

													A_ 						=		(self.timesteps == timestep).nonzero().item()
													A_ 						=		self.sigmas[step_index]

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

													A_ 						=		randn_tensor(
													    model_output.shape   ,     dtype=model_output.dtype   ,     device=model_output.device   ,     generator=lowerCAmelCase  )

													A_ 						=		noise * s_noise
													A_ 						=		sigma * (gamma + 1)

													if gamma > 0:
																				A_ 						=		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":
																				A_ 						=		model_output
													elif self.config.prediction_type == "epsilon":
																				A_ 						=		sample - sigma_hat * 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))
													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_hat

													A_ 						=		self.sigmas[step_index + 1] - sigma_hat

													A_ 						=		sample + derivative * dt

													if not return_dict:
																				return (prev_sample,)

													return EulerDiscreteSchedulerOutput(prev_sample=lowerCAmelCase   ,     pred_original_sample=lowerCAmelCase  )






						def 							_UpperCAmelCase					(     self       :			Optional[Any]   ,     lowerCAmelCase       :			torch.FloatTensor   ,     lowerCAmelCase       :			torch.FloatTensor   ,     lowerCAmelCase       :			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(lowerCAmelCase  ):
																				# 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       :			int  ):
													return self.config.num_train_timesteps









'''simple docstring'''
def 			a_							(  UpperCamelCase_	,     UpperCamelCase_ = 1_0_0_0   ):
							if (not isinstance(UpperCamelCase_	,     UpperCamelCase_   )) or (digit_position <= 0):
														raise ValueError("Digit position must be a positive integer"   )
							elif (not isinstance(UpperCamelCase_	,     UpperCamelCase_   )) or (precision < 0):
														raise ValueError("Precision must be a nonnegative integer"   )

							# compute an approximation of (16 ** (n - 1)) * pi whose fractional part is mostly
							# accurate
							A_ 						=		(
							    4 * _subsum(UpperCamelCase_	,     1	,     UpperCamelCase_   )
							    - 2 * _subsum(UpperCamelCase_	,     4	,     UpperCamelCase_   )
							    - _subsum(UpperCamelCase_	,     5	,     UpperCamelCase_   )
							    - _subsum(UpperCamelCase_	,     6	,     UpperCamelCase_   )
							)

							# return the first hex digit of the fractional part of the result
							return hex(int((sum_result % 1) * 1_6   )   )[2:]







def 			a_							(  UpperCamelCase_	,     UpperCamelCase_	,     UpperCamelCase_   ):
							A_ 						=		0.0
							for sum_index in range(digit_pos_to_extract + precision   ):
														A_ 						=		8 * sum_index + denominator_addend
														if sum_index < digit_pos_to_extract:
																					# if the exponential term is an integer and we mod it by the denominator
																					# before dividing, only the integer part of the sum will change;
																					# the fractional part will not
																					A_ 						=		pow(
																					    1_6	,     digit_pos_to_extract - 1 - sum_index	,     UpperCamelCase_   )
														else:
																					A_ 						=		pow(1_6	,     digit_pos_to_extract - 1 - sum_index   )
														total += exponential_term / denominator
							return total


if __name__ == "__main__":
							import doctest

							doctest.testmod()





