
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


A__       :   Tuple   						=					logging.get_logger(__name__)  # pylint: disable=invalid-name





@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerDiscrete
class 						lowercase       (  __UpperCamelCase					):
					__a					=    42
					__a					=    None





def      _a     (   __UpperCamelCase       :  Tuple	,__UpperCamelCase       :  str=0.999	,__UpperCamelCase       :  Union[str, Any]="cosine"	,):
			if alpha_transform_type == "cosine":

						def alpha_bar_fn(__UpperCamelCase       :  List[str]    ):
									return math.cos((t + 0.008) / 1.008 * math.pi / 2    ) ** 2

			elif alpha_transform_type == "exp":

						def alpha_bar_fn(__UpperCamelCase       :  Optional[Any]    ):
									return math.exp(t * -12.0    )

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

			lowerCAmelCase__ :    Dict				      =			[]
			for i in range(__UpperCamelCase    ):
						lowerCAmelCase__ :    int				      =			i / num_diffusion_timesteps
						lowerCAmelCase__ :    Dict				      =			(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       (  __UpperCamelCase	,		__UpperCamelCase					):
					__a					=    [e.name for e in KarrasDiffusionSchedulers]
					__a					=    1
					@register_to_config
					def __init__(		self ,	SCREAMING_SNAKE_CASE__ = 1000 ,	SCREAMING_SNAKE_CASE__ = 0.0_001 ,	SCREAMING_SNAKE_CASE__ = 0.02 ,	SCREAMING_SNAKE_CASE__ = "linear" ,	SCREAMING_SNAKE_CASE__ = None ,	SCREAMING_SNAKE_CASE__ = "epsilon" ,	SCREAMING_SNAKE_CASE__ = "linear" ,	SCREAMING_SNAKE_CASE__ = False ,	SCREAMING_SNAKE_CASE__ = "linspace" ,	SCREAMING_SNAKE_CASE__ = 0 ,	):
								"""simple docstring"""







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

								lowerCAmelCase__ :    List[Any]				      =			1.0 - self.betas
								lowerCAmelCase__ :    str				      =			torch.cumprod(self.alphas ,	dim=0    )

								lowerCAmelCase__ :    Optional[int]				      =			np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5    )
								lowerCAmelCase__ :    Any				      =			np.concatenate([sigmas[::-1], [0.0]]    ).astype(np.floataa    )
								lowerCAmelCase__ :    Dict				      =			torch.from_numpy(SCREAMING_SNAKE_CASE__    )

								# setable values
								lowerCAmelCase__ :    Any				      =			None
								lowerCAmelCase__ :    List[str]				      =			np.linspace(0 ,	num_train_timesteps - 1 ,	SCREAMING_SNAKE_CASE__ ,	dtype=SCREAMING_SNAKE_CASE__    )[::-1].copy()
								lowerCAmelCase__ :    Any				      =			torch.from_numpy(SCREAMING_SNAKE_CASE__    )
								lowerCAmelCase__ :    Tuple				      =			False
								lowerCAmelCase__ :    List[Any]				      =			use_karras_sigmas
					@property
					def lowercase_			(		self    ):
								"""simple docstring"""







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

								return (self.sigmas.max() ** 2 + 1) ** 0.5
					def lowercase_			(		self ,	SCREAMING_SNAKE_CASE__ ,	SCREAMING_SNAKE_CASE__    ):
								"""simple docstring"""







								if isinstance(SCREAMING_SNAKE_CASE__ ,	torch.Tensor    ):
											lowerCAmelCase__ :    Optional[Any]				      =			timestep.to(self.timesteps.device    )
								lowerCAmelCase__ :    Optional[int]				      =			(self.timesteps == timestep).nonzero().item()
								lowerCAmelCase__ :    List[Any]				      =			self.sigmas[step_index]

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

								lowerCAmelCase__ :    int				      =			True
								return sample
					def lowercase_			(		self ,	SCREAMING_SNAKE_CASE__ ,	SCREAMING_SNAKE_CASE__ = None    ):
								"""simple docstring"""







								lowerCAmelCase__ :    Tuple				      =			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__ :    List[Any]				      =			np.linspace(0 ,	self.config.num_train_timesteps - 1 ,	SCREAMING_SNAKE_CASE__ ,	dtype=SCREAMING_SNAKE_CASE__    )[
											    ::-1
											].copy()
								elif self.config.timestep_spacing == "leading":
											lowerCAmelCase__ :    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
											lowerCAmelCase__ :    List[Any]				      =			(np.arange(0 ,	SCREAMING_SNAKE_CASE__    ) * step_ratio).round()[::-1].copy().astype(SCREAMING_SNAKE_CASE__    )
											timesteps += self.config.steps_offset
								elif self.config.timestep_spacing == "trailing":
											lowerCAmelCase__ :    Optional[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
											lowerCAmelCase__ :    List[str]				      =			(np.arange(self.config.num_train_timesteps ,	0 ,	-step_ratio    )).round().copy().astype(SCREAMING_SNAKE_CASE__    )
											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__ :    Dict				      =			np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5    )
								lowerCAmelCase__ :    Union[str, Any]				      =			np.log(SCREAMING_SNAKE_CASE__    )

								if self.config.interpolation_type == "linear":
											lowerCAmelCase__ :    Dict				      =			np.interp(SCREAMING_SNAKE_CASE__ ,	np.arange(0 ,	len(SCREAMING_SNAKE_CASE__    )    ) ,	SCREAMING_SNAKE_CASE__    )
								elif self.config.interpolation_type == "log_linear":
											lowerCAmelCase__ :    List[Any]				      =			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:
											lowerCAmelCase__ :    Any				      =			self._convert_to_karras(in_sigmas=SCREAMING_SNAKE_CASE__ ,	num_inference_steps=self.num_inference_steps    )
											lowerCAmelCase__ :    str				      =			np.array([self._sigma_to_t(SCREAMING_SNAKE_CASE__ ,	SCREAMING_SNAKE_CASE__    ) for sigma in sigmas]    )

								lowerCAmelCase__ :    Dict				      =			np.concatenate([sigmas, [0.0]]    ).astype(np.floataa    )
								lowerCAmelCase__ :    Tuple				      =			torch.from_numpy(SCREAMING_SNAKE_CASE__    ).to(device=SCREAMING_SNAKE_CASE__    )
								if str(SCREAMING_SNAKE_CASE__    ).startswith('''mps'''    ):
											# mps does not support float64
											lowerCAmelCase__ :    Optional[Any]				      =			torch.from_numpy(SCREAMING_SNAKE_CASE__    ).to(SCREAMING_SNAKE_CASE__ ,	dtype=torch.floataa    )
								else:
											lowerCAmelCase__ :    Optional[Any]				      =			torch.from_numpy(SCREAMING_SNAKE_CASE__    ).to(device=SCREAMING_SNAKE_CASE__    )
					def lowercase_			(		self ,	SCREAMING_SNAKE_CASE__ ,	SCREAMING_SNAKE_CASE__    ):
								"""simple docstring"""







								lowerCAmelCase__ :    Tuple				      =			np.log(SCREAMING_SNAKE_CASE__    )

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

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

								lowerCAmelCase__ :    Dict				      =			log_sigmas[low_idx]
								lowerCAmelCase__ :    Optional[int]				      =			log_sigmas[high_idx]

								# interpolate sigmas
								lowerCAmelCase__ :    List[Any]				      =			(low - log_sigma) / (low - high)
								lowerCAmelCase__ :    Tuple				      =			np.clip(SCREAMING_SNAKE_CASE__ ,	0 ,	1    )

								# transform interpolation to time range
								lowerCAmelCase__ :    Optional[int]				      =			(1 - w) * low_idx + w * high_idx
								lowerCAmelCase__ :    Tuple				      =			t.reshape(sigma.shape    )
								return t
					def lowercase_			(		self ,	SCREAMING_SNAKE_CASE__ ,	SCREAMING_SNAKE_CASE__    ):
								"""simple docstring"""







								lowerCAmelCase__ :    float				      =			in_sigmas[-1].item()
								lowerCAmelCase__ :    float				      =			in_sigmas[0].item()

								lowerCAmelCase__ :    List[str]				      =			7.0  # 7.0 is the value used in the paper
								lowerCAmelCase__ :    str				      =			np.linspace(0 ,	1 ,	SCREAMING_SNAKE_CASE__    )
								lowerCAmelCase__ :    List[Any]				      =			sigma_min ** (1 / rho)
								lowerCAmelCase__ :    Optional[int]				      =			sigma_max ** (1 / rho)
								lowerCAmelCase__ :    Union[str, Any]				      =			(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
								return sigmas
					def lowercase_			(		self ,	SCREAMING_SNAKE_CASE__ ,	SCREAMING_SNAKE_CASE__ ,	SCREAMING_SNAKE_CASE__ ,	SCREAMING_SNAKE_CASE__ = 0.0 ,	SCREAMING_SNAKE_CASE__ = 0.0 ,	SCREAMING_SNAKE_CASE__ = float('''inf'''    ) ,	SCREAMING_SNAKE_CASE__ = 1.0 ,	SCREAMING_SNAKE_CASE__ = None ,	SCREAMING_SNAKE_CASE__ = True ,	):
								"""simple docstring"""







								if (
								    isinstance(SCREAMING_SNAKE_CASE__ ,	SCREAMING_SNAKE_CASE__    )
								    or isinstance(SCREAMING_SNAKE_CASE__ ,	torch.IntTensor    )
								    or isinstance(SCREAMING_SNAKE_CASE__ ,	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(SCREAMING_SNAKE_CASE__ ,	torch.Tensor    ):
											lowerCAmelCase__ :    Any				      =			timestep.to(self.timesteps.device    )

								lowerCAmelCase__ :    Optional[Any]				      =			(self.timesteps == timestep).nonzero().item()
								lowerCAmelCase__ :    Tuple				      =			self.sigmas[step_index]

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

								lowerCAmelCase__ :    Tuple				      =			randn_tensor(
								    model_output.shape ,	dtype=model_output.dtype ,	device=model_output.device ,	generator=SCREAMING_SNAKE_CASE__    )

								lowerCAmelCase__ :    Dict				      =			noise * s_noise
								lowerCAmelCase__ :    Any				      =			sigma * (gamma + 1)

								if gamma > 0:
											lowerCAmelCase__ :    int				      =			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":
											lowerCAmelCase__ :    str				      =			model_output
								elif self.config.prediction_type == "epsilon":
											lowerCAmelCase__ :    Tuple				      =			sample - sigma_hat * model_output
								elif self.config.prediction_type == "v_prediction":
											# * c_out + input * c_skip
											lowerCAmelCase__ :    Optional[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
								lowerCAmelCase__ :    List[Any]				      =			(sample - pred_original_sample) / sigma_hat

								lowerCAmelCase__ :    int				      =			self.sigmas[step_index + 1] - sigma_hat

								lowerCAmelCase__ :    int				      =			sample + derivative * dt

								if not return_dict:
											return (prev_sample,)

								return EulerDiscreteSchedulerOutput(prev_sample=SCREAMING_SNAKE_CASE__ ,	pred_original_sample=SCREAMING_SNAKE_CASE__    )
					def lowercase_			(		self ,	SCREAMING_SNAKE_CASE__ ,	SCREAMING_SNAKE_CASE__ ,	SCREAMING_SNAKE_CASE__ ,	):
								"""simple docstring"""







								lowerCAmelCase__ :    int				      =			self.sigmas.to(device=original_samples.device ,	dtype=original_samples.dtype    )
								if original_samples.device.type == "mps" and torch.is_floating_point(SCREAMING_SNAKE_CASE__    ):
											# mps does not support float64
											lowerCAmelCase__ :    Any				      =			self.timesteps.to(original_samples.device ,	dtype=torch.floataa    )
											lowerCAmelCase__ :    int				      =			timesteps.to(original_samples.device ,	dtype=torch.floataa    )
								else:
											lowerCAmelCase__ :    List[str]				      =			self.timesteps.to(original_samples.device    )
											lowerCAmelCase__ :    Optional[Any]				      =			timesteps.to(original_samples.device    )

								lowerCAmelCase__ :    Tuple				      =			[(schedule_timesteps == t).nonzero().item() for t in timesteps]

								lowerCAmelCase__ :    Optional[Any]				      =			sigmas[step_indices].flatten()
								while len(sigma.shape    ) < len(original_samples.shape    ):
											lowerCAmelCase__ :    str				      =			sigma.unsqueeze(-1    )

								lowerCAmelCase__ :    Optional[int]				      =			original_samples + noise * sigma
								return noisy_samples
					def __len__(		self    ):
								"""simple docstring"""







								return self.config.num_train_timesteps





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



def      _a     (   __UpperCamelCase       :  NDArray[floataa]	,__UpperCamelCase       :  NDArray[floataa]    ):
			lowerCAmelCase__      ,				lowerCAmelCase__ :    Any				      =			np.shape(__UpperCamelCase    )

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

						lowerCAmelCase__ :    int				      =			(vector[row] - total) / coefficients[row, row]

			return x



def      _a     (   __UpperCamelCase       :  NDArray[floataa]	,__UpperCamelCase       :  NDArray[floataa]    ):
			lowerCAmelCase__      ,				lowerCAmelCase__ :    str				      =			np.shape(__UpperCamelCase    )
			if rows != columns:
						return np.array(()	,dtype=__UpperCamelCase    )

			# augmented matrix
			lowerCAmelCase__ :    NDArray[floataa]				      =			np.concatenate((coefficients, vector)	,axis=1    )
			lowerCAmelCase__ :    List[str]				      =			augmented_mat.astype('''float64'''    )

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

			lowerCAmelCase__ :    int				      =			retroactive_resolution(
			    augmented_mat[:, 0:columns]	,augmented_mat[:, columns : columns + 1]    )

			return x


if __name__ == "__main__":
							import doctest

							doctest.testmod()



