





'''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


snake_case_       :    Dict          =					logging.get_logger(__name__)  # pylint: disable=invalid-name


@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerAncestralDiscrete
class    __a (lowerCAmelCase__       ):
							__a   :				torch.FloatTensor
							__a   :				Optional[torch.FloatTensor]       =    None





def     lowerCamelCase_ (					SCREAMING_SNAKE_CASE__ :     str,     SCREAMING_SNAKE_CASE__ :     int=0.9_99,     SCREAMING_SNAKE_CASE__ :     Union[str, Any]="cosine",     )	->		List[str]:
						if alpha_transform_type == "cosine":

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

						elif alpha_transform_type == "exp":

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

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

						UpperCAmelCase_     : Optional[int]         =					[]
						for i in range(SCREAMING_SNAKE_CASE__				):
												UpperCAmelCase_     : int         =					i / num_diffusion_timesteps
												UpperCAmelCase_     : Union[str, 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    __a (lowerCAmelCase__    ,						lowerCAmelCase__       ):
							__a   :				str       =    [e.name for e in KarrasDiffusionSchedulers]
							__a   :				Union[str, Any]       =    1

							@register_to_config
							def __init__(							self							:       str    ,       __magic_name__							:       int = 10_00    ,       __magic_name__							:       float = 0.0_0_0_1    ,       __magic_name__							:       float = 0.0_2    ,       __magic_name__							:       str = "linear"    ,       __magic_name__							:       Optional[Union[np.ndarray, List[float]]] = None    ,       __magic_name__							:       str = "epsilon"    ,       __magic_name__							:       str = "linspace"    ,       __magic_name__							:       int = 0    ,       )   ->    int:







													"""simple docstring"""


													if trained_betas is not None:
																			UpperCAmelCase_     : Optional[int]         =					torch.tensor(_UpperCAmelCase    ,       dtype=torch.floataa				)
													elif beta_schedule == "linear":
																			UpperCAmelCase_     : Tuple         =					torch.linspace(_UpperCAmelCase    ,       _UpperCAmelCase    ,       _UpperCAmelCase    ,       dtype=torch.floataa				)
													elif beta_schedule == "scaled_linear":
																			# this schedule is very specific to the latent diffusion model.
																			UpperCAmelCase_     : List[Any]         =					(
																			    torch.linspace(beta_start**0.5    ,       beta_end**0.5    ,       _UpperCAmelCase    ,       dtype=torch.floataa				) ** 2
																			)
													elif beta_schedule == "squaredcos_cap_v2":
																			# Glide cosine schedule
																			UpperCAmelCase_     : str         =					betas_for_alpha_bar(_UpperCAmelCase				)
													else:
																			raise NotImplementedError(F"""{beta_schedule} does is not implemented for {self.__class__}"""				)

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

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

													# setable values
													UpperCAmelCase_     : str         =					None
													UpperCAmelCase_     : Union[str, Any]         =					np.linspace(0    ,       num_train_timesteps - 1    ,       _UpperCAmelCase    ,       dtype=_UpperCAmelCase				)[::-1].copy()
													UpperCAmelCase_     : Tuple         =					torch.from_numpy(_UpperCAmelCase				)
													UpperCAmelCase_     : Optional[int]         =					False

							@property
							def       UpperCAmelCase__		(							self							:       List[str]				)   ->    Optional[int]:







													"""simple docstring"""


													if self.config.timestep_spacing in ["linspace", "trailing"]:
																			return self.sigmas.max()

													return (self.sigmas.max() ** 2 + 1) ** 0.5

							def       UpperCAmelCase__		(							self							:       int    ,       __magic_name__							:       torch.FloatTensor    ,       __magic_name__							:       Union[float, torch.FloatTensor]				)   ->    torch.FloatTensor:







													"""simple docstring"""


													if isinstance(_UpperCAmelCase    ,       torch.Tensor				):
																			UpperCAmelCase_     : Any         =					timestep.to(self.timesteps.device				)
													UpperCAmelCase_     : Dict         =					(self.timesteps == timestep).nonzero().item()
													UpperCAmelCase_     : Tuple         =					self.sigmas[step_index]
													UpperCAmelCase_     : Any         =					sample / ((sigma**2 + 1) ** 0.5)
													UpperCAmelCase_     : Optional[int]         =					True
													return sample

							def       UpperCAmelCase__		(							self							:       int    ,       __magic_name__							:       int    ,       __magic_name__							:       Union[str, torch.device] = None				)   ->    Any:







													"""simple docstring"""
													UpperCAmelCase_     : Optional[int]         =					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_     : List[Any]         =					np.linspace(0    ,       self.config.num_train_timesteps - 1    ,       _UpperCAmelCase    ,       dtype=_UpperCAmelCase				)[
																			    ::-1
																			].copy()
													elif self.config.timestep_spacing == "leading":
																			UpperCAmelCase_     : Union[str, Any]         =					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_     : Any         =					(np.arange(0    ,       _UpperCAmelCase				) * step_ratio).round()[::-1].copy().astype(_UpperCAmelCase				)
																			timesteps += self.config.steps_offset
													elif self.config.timestep_spacing == "trailing":
																			UpperCAmelCase_     : Tuple         =					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_     : int         =					(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'."""				)

													UpperCAmelCase_     : int         =					np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5				)
													UpperCAmelCase_     : Dict         =					np.interp(_UpperCAmelCase    ,       np.arange(0    ,       len(_UpperCAmelCase				)				)    ,       _UpperCAmelCase				)
													UpperCAmelCase_     : List[str]         =					np.concatenate([sigmas, [0.0]]				).astype(np.floataa				)
													UpperCAmelCase_     : Optional[int]         =					torch.from_numpy(_UpperCAmelCase				).to(device=_UpperCAmelCase				)
													if str(_UpperCAmelCase				).startswith('''mps'''				):
																			# mps does not support float64
																			UpperCAmelCase_     : List[str]         =					torch.from_numpy(_UpperCAmelCase				).to(_UpperCAmelCase    ,       dtype=torch.floataa				)
													else:
																			UpperCAmelCase_     : int         =					torch.from_numpy(_UpperCAmelCase				).to(device=_UpperCAmelCase				)

							def       UpperCAmelCase__		(							self							:       List[Any]    ,       __magic_name__							:       torch.FloatTensor    ,       __magic_name__							:       Union[float, torch.FloatTensor]    ,       __magic_name__							:       torch.FloatTensor    ,       __magic_name__							:       Optional[torch.Generator] = None    ,       __magic_name__							:       bool = True    ,       )   ->    Union[EulerAncestralDiscreteSchedulerOutput, Tuple]:







													"""simple docstring"""


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

													UpperCAmelCase_     : Optional[int]         =					(self.timesteps == timestep).nonzero().item()
													UpperCAmelCase_     : Dict         =					self.sigmas[step_index]

													# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
													if self.config.prediction_type == "epsilon":
																			UpperCAmelCase_     : Tuple         =					sample - sigma * model_output
													elif self.config.prediction_type == "v_prediction":
																			# * c_out + input * c_skip
																			UpperCAmelCase_     : List[Any]         =					model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
													elif self.config.prediction_type == "sample":
																			raise NotImplementedError('''prediction_type not implemented yet: sample'''				)
													else:
																			raise ValueError(
																			    F"""prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"""				)

													UpperCAmelCase_     : int         =					self.sigmas[step_index]
													UpperCAmelCase_     : List[Any]         =					self.sigmas[step_index + 1]
													UpperCAmelCase_     : Dict         =					(sigma_to**2 * (sigma_from**2 - sigma_to**2) / sigma_from**2) ** 0.5
													UpperCAmelCase_     : List[str]         =					(sigma_to**2 - sigma_up**2) ** 0.5

													# 2. Convert to an ODE derivative
													UpperCAmelCase_     : Union[str, Any]         =					(sample - pred_original_sample) / sigma

													UpperCAmelCase_     : Dict         =					sigma_down - sigma

													UpperCAmelCase_     : Optional[Any]         =					sample + derivative * dt

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

													UpperCAmelCase_     : int         =					prev_sample + noise * sigma_up

													if not return_dict:
																			return (prev_sample,)

													return EulerAncestralDiscreteSchedulerOutput(
													    prev_sample=_UpperCAmelCase    ,       pred_original_sample=_UpperCAmelCase				)

							def       UpperCAmelCase__		(							self							:       List[str]    ,       __magic_name__							:       torch.FloatTensor    ,       __magic_name__							:       torch.FloatTensor    ,       __magic_name__							:       torch.FloatTensor    ,       )   ->    torch.FloatTensor:







													"""simple docstring"""
													UpperCAmelCase_     : Dict         =					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
																			UpperCAmelCase_     : Union[str, Any]         =					self.timesteps.to(original_samples.device    ,       dtype=torch.floataa				)
																			UpperCAmelCase_     : Optional[Any]         =					timesteps.to(original_samples.device    ,       dtype=torch.floataa				)
													else:
																			UpperCAmelCase_     : List[str]         =					self.timesteps.to(original_samples.device				)
																			UpperCAmelCase_     : Optional[int]         =					timesteps.to(original_samples.device				)

													UpperCAmelCase_     : str         =					[(schedule_timesteps == t).nonzero().item() for t in timesteps]

													UpperCAmelCase_     : Tuple         =					sigmas[step_indices].flatten()
													while len(sigma.shape				) < len(original_samples.shape				):
																			UpperCAmelCase_     : Union[str, Any]         =					sigma.unsqueeze(-1				)

													UpperCAmelCase_     : Optional[int]         =					original_samples + noise * sigma
													return noisy_samples



							def __len__(							self							:       str				)   ->    str:







													"""simple docstring"""
													return self.config.num_train_timesteps







'''simple docstring'''







import numpy as np
from numpy import floataa
from numpy.typing import NDArray





def     lowerCamelCase_ (					SCREAMING_SNAKE_CASE__ :     NDArray[floataa],     SCREAMING_SNAKE_CASE__ :     NDArray[floataa]				)	->		NDArray[floataa]:
						UpperCAmelCase_  ,    UpperCAmelCase_     : Any         =					np.shape(SCREAMING_SNAKE_CASE__				)

						UpperCAmelCase_     : NDArray[floataa]         =					np.zeros((rows, 1),     dtype=SCREAMING_SNAKE_CASE__				)
						for row in reversed(range(SCREAMING_SNAKE_CASE__				)				):
												UpperCAmelCase_     : Union[str, Any]         =					0
												for col in range(row + 1,     SCREAMING_SNAKE_CASE__				):
																		total += coefficients[row, col] * x[col]

												UpperCAmelCase_     : str         =					(vector[row] - total) / coefficients[row, row]

						return x





def     lowerCamelCase_ (					SCREAMING_SNAKE_CASE__ :     NDArray[floataa],     SCREAMING_SNAKE_CASE__ :     NDArray[floataa]				)	->		NDArray[floataa]:
						UpperCAmelCase_  ,    UpperCAmelCase_     : List[Any]         =					np.shape(SCREAMING_SNAKE_CASE__				)
						if rows != columns:
												return np.array((),     dtype=SCREAMING_SNAKE_CASE__				)

						# augmented matrix
						UpperCAmelCase_     : NDArray[floataa]         =					np.concatenate((coefficients, vector),     axis=1				)
						UpperCAmelCase_     : Optional[Any]         =					augmented_mat.astype('''float64'''				)

						# scale the matrix leaving it triangular
						for row in range(rows - 1				):
												UpperCAmelCase_     : Optional[int]         =					augmented_mat[row, row]
												for col in range(row + 1,     SCREAMING_SNAKE_CASE__				):
																		UpperCAmelCase_     : Optional[Any]         =					augmented_mat[col, row] / pivot
																		augmented_mat[col, :] -= factor * augmented_mat[row, :]

						UpperCAmelCase_     : Optional[Any]         =					retroactive_resolution(
						    augmented_mat[:, 0:columns],     augmented_mat[:, columns : columns + 1]				)

						return x


if __name__ == "__main__":
					import doctest

					doctest.testmod()





