"""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


UpperCamelCase_							:							List[str]				 =		logging.get_logger(__name__)  # pylint: disable=invalid-name


@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerDiscrete
class       _lowercase		( __lowerCamelCase	):
				lowerCamelCase__							=							42
				lowerCamelCase__							=							None


def 	a__   (		UpperCAmelCase__							:      Tuple		,      UpperCAmelCase__							:      Union[str, Any]=0.9_99		,      UpperCAmelCase__							:      Optional[int]="cosine"		,      )->						Dict:
						if alpha_transform_type == "cosine":

												def alpha_bar_fn(UpperCAmelCase__							:      str      ):
																		return math.cos((t + 0.0_08) / 1.0_08 * math.pi / 2      ) ** 2

						elif alpha_transform_type == "exp":

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

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

						UpperCAmelCase__       						=		[]
						for i in range(UpperCAmelCase__      ):
												UpperCAmelCase__       						=		i / num_diffusion_timesteps
												UpperCAmelCase__       						=		(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       _lowercase		( __lowerCamelCase   ,   __lowerCamelCase	):
				lowerCamelCase__							=							[e.name for e in KarrasDiffusionSchedulers]
				lowerCamelCase__							=							1

				@register_to_config
				def __init__(  self							:     Tuple							,     _lowercase							:     int = 1_0_0_0							,     _lowercase							:     float = 0.0001							,     _lowercase							:     float = 0.02							,     _lowercase							:     str = "linear"							,     _lowercase							:     Optional[Union[np.ndarray, List[float]]] = None							,     _lowercase							:     str = "epsilon"							,     _lowercase							:     str = "linear"							,     _lowercase							:     Optional[bool] = False							,     _lowercase							:     str = "linspace"							,     _lowercase							:     int = 0							,     ):


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

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

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

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

				@property
				def 							A			(  self							:     str  ):


										'''simple docstring'''
										# 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							:     Tuple							,     _lowercase							:     torch.FloatTensor							,     _lowercase							:     Union[float, torch.FloatTensor]  ):


										'''simple docstring'''
										if isinstance(_lowercase							,     torch.Tensor  ):
																UpperCAmelCase__       						=		timestep.to(self.timesteps.device  )
										UpperCAmelCase__       						=		(self.timesteps == timestep).nonzero().item()
										UpperCAmelCase__       						=		self.sigmas[step_index]

										UpperCAmelCase__       						=		sample / ((sigma**2 + 1) ** 0.5)

										UpperCAmelCase__       						=		True
										return sample

				def 							A			(  self							:     Optional[int]							,     _lowercase							:     int							,     _lowercase							:     Union[str, torch.device] = None  ):


										'''simple docstring'''
										UpperCAmelCase__       						=		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__       						=		np.linspace(0							,     self.config.num_train_timesteps - 1							,     _lowercase							,     dtype=_lowercase  )[
																    ::-1
																].copy()
										elif self.config.timestep_spacing == "leading":
																UpperCAmelCase__       						=		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__       						=		(np.arange(0							,     _lowercase  ) * step_ratio).round()[::-1].copy().astype(_lowercase  )
																timesteps += self.config.steps_offset
										elif self.config.timestep_spacing == "trailing":
																UpperCAmelCase__       						=		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__       						=		(np.arange(self.config.num_train_timesteps							,     0							,     -step_ratio  )).round().copy().astype(_lowercase  )
																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__       						=		np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5  )
										UpperCAmelCase__       						=		np.log(_lowercase  )

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

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

				def 							A			(  self							:     Tuple							,     _lowercase							:     Tuple							,     _lowercase							:     Dict  ):


										'''simple docstring'''
										# get log sigma
										UpperCAmelCase__       						=		np.log(_lowercase  )

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

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

										UpperCAmelCase__       						=		log_sigmas[low_idx]
										UpperCAmelCase__       						=		log_sigmas[high_idx]

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

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

				def 							A			(  self							:     Dict							,     _lowercase							:     torch.FloatTensor							,     _lowercase							:     Optional[int]  ):


										'''simple docstring'''
										UpperCAmelCase__       						=		in_sigmas[-1].item()
										UpperCAmelCase__       						=		in_sigmas[0].item()

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

				def 							A			(  self							:     int							,     _lowercase							:     torch.FloatTensor							,     _lowercase							:     Union[float, torch.FloatTensor]							,     _lowercase							:     torch.FloatTensor							,     _lowercase							:     float = 0.0							,     _lowercase							:     float = 0.0							,     _lowercase							:     float = float("""inf"""  )							,     _lowercase							:     float = 1.0							,     _lowercase							:     Optional[torch.Generator] = None							,     _lowercase							:     bool = True							,     ):


										'''simple docstring'''

										if (
										    isinstance(_lowercase							,     _lowercase  )
										    or isinstance(_lowercase							,     torch.IntTensor  )
										    or isinstance(_lowercase							,     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(_lowercase							,     torch.Tensor  ):
																UpperCAmelCase__       						=		timestep.to(self.timesteps.device  )

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

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

										UpperCAmelCase__       						=		randn_tensor(
										    model_output.shape							,     dtype=model_output.dtype							,     device=model_output.device							,     generator=_lowercase  )

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

										if gamma > 0:
																UpperCAmelCase__       						=		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__       						=		model_output
										elif self.config.prediction_type == "epsilon":
																UpperCAmelCase__       						=		sample - sigma_hat * model_output
										elif self.config.prediction_type == "v_prediction":
																# * c_out + input * c_skip
																UpperCAmelCase__       						=		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__       						=		(sample - pred_original_sample) / sigma_hat

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

										UpperCAmelCase__       						=		sample + derivative * dt

										if not return_dict:
																return (prev_sample,)

										return EulerDiscreteSchedulerOutput(prev_sample=_lowercase							,     pred_original_sample=_lowercase  )

				def 							A			(  self							:     List[str]							,     _lowercase							:     torch.FloatTensor							,     _lowercase							:     torch.FloatTensor							,     _lowercase							:     torch.FloatTensor							,     ):


										'''simple docstring'''
										# Make sure sigmas and timesteps have the same device and dtype as original_samples
										UpperCAmelCase__       						=		self.sigmas.to(device=original_samples.device							,     dtype=original_samples.dtype  )
										if original_samples.device.type == "mps" and torch.is_floating_point(_lowercase  ):
																# mps does not support float64
																UpperCAmelCase__       						=		self.timesteps.to(original_samples.device							,     dtype=torch.floataa  )
																UpperCAmelCase__       						=		timesteps.to(original_samples.device							,     dtype=torch.floataa  )
										else:
																UpperCAmelCase__       						=		self.timesteps.to(original_samples.device  )
																UpperCAmelCase__       						=		timesteps.to(original_samples.device  )

										UpperCAmelCase__       						=		[(schedule_timesteps == t).nonzero().item() for t in timesteps]

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

										UpperCAmelCase__       						=		original_samples + noise * sigma
										return noisy_samples

				def __len__(  self							:     int  ):


										'''simple docstring'''
										return self.config.num_train_timesteps


"""simple docstring"""







from __future__ import annotations


def 	a__   (		UpperCAmelCase__							:      list      )->						int | float:
						UpperCAmelCase__       						=		sorted(UpperCAmelCase__      )
						UpperCAmelCase__       						=		len(UpperCAmelCase__      )
						UpperCAmelCase__       						=		length >> 1
						return (
						    (sorted_list[mid_index] + sorted_list[mid_index - 1]) / 2
						    if length % 2 == 0
						    else sorted_list[mid_index]
						)


def 	a__   (		)->						Dict:
						import doctest

						doctest.testmod()


if __name__ == "__main__":
						main()

