



'''simple docstring'''
from math import cos, sin






def A__					(  UpperCAmelCase_							):
						_UpperCamelCase      :	List[str]				       =     float(UpperCAmelCase_							)
						return [[scaling_factor * int(x == y							) for x in range(2							)] for y in range(2							)]






def A__					(  UpperCAmelCase_							):
						_UpperCamelCase       ,    _UpperCamelCase      :	Optional[int]				       =     cos(UpperCAmelCase_							), sin(UpperCAmelCase_							)
						return [[c, -s], [s, c]]






def A__					(  UpperCAmelCase_							):
						_UpperCamelCase       ,    _UpperCamelCase      :	Optional[Any]				       =     cos(UpperCAmelCase_							), sin(UpperCAmelCase_							)
						_UpperCamelCase      :	List[str]				       =     c * s
						return [[c * c, cs], [cs, s * s]]






def A__					(  UpperCAmelCase_							):
						_UpperCamelCase       ,    _UpperCamelCase      :	int				       =     cos(UpperCAmelCase_							), sin(UpperCAmelCase_							)
						_UpperCamelCase      :	Optional[Any]				       =     c * s
						return [[2 * c - 1, 2 * cs], [2 * cs, 2 * s - 1]]


print(F"""    {scaling(5) = }""")
print(F"""  {rotation(45) = }""")
print(F"""{projection(45) = }""")

print(F"""{reflection(45) = }""")







'''simple docstring'''
import math
import warnings
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch
from scipy import integrate

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






@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->LMSDiscrete
class 							lowercase__			(							lowercase     ):
	lowercase__						       =    42
	lowercase__						       =    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}'							)

						_UpperCamelCase      :	Tuple				       =     []
						for i in range(UpperCAmelCase_							):
												_UpperCamelCase      :	List[str]				       =     i / num_diffusion_timesteps
												_UpperCamelCase      :	Optional[int]				       =     (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__			(							lowercase		,      lowercase     ):
	lowercase__						       =    [e.name for e in KarrasDiffusionSchedulers]
	lowercase__						       =    1





	@register_to_config
	def __init__(				self      :       int				,lowerCamelCase__      :       int = 1000				,lowerCamelCase__      :       float = 0.0_0_0_1				,lowerCamelCase__      :       float = 0.0_2				,lowerCamelCase__      :       str = "linear"				,lowerCamelCase__      :       Optional[Union[np.ndarray, List[float]]] = None				,lowerCamelCase__      :       Optional[bool] = False				,lowerCamelCase__      :       str = "epsilon"				,lowerCamelCase__      :       str = "linspace"				,lowerCamelCase__      :       int = 0				,):







							'''simple docstring'''
							if trained_betas is not None:
													_UpperCamelCase      :	Union[str, Any]				       =     torch.tensor(lowerCamelCase__				,dtype=torch.floataa				)
							elif beta_schedule == "linear":
													_UpperCamelCase      :	Union[str, Any]				       =     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      :	Dict				       =     betas_for_alpha_bar(lowerCamelCase__				)
							else:
													raise NotImplementedError(F'{beta_schedule} does is not implemented for {self.__class__}'				)

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

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

							# setable values
							_UpperCamelCase      :	List[str]				       =     None
							_UpperCamelCase      :	List[Any]				       =     use_karras_sigmas
							self.set_timesteps(lowerCamelCase__				,lowerCamelCase__				)
							_UpperCamelCase      :	Any				       =     []
							_UpperCamelCase      :	Tuple				       =     False





	@property
	def 			UpperCamelCase_						(				self      :       Union[str, Any]				):







							'''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 			UpperCamelCase_						(				self      :       Optional[int]				,lowerCamelCase__      :       torch.FloatTensor				,lowerCamelCase__      :       Union[float, torch.FloatTensor]				):







							'''simple docstring'''
							if isinstance(lowerCamelCase__				,torch.Tensor				):
													_UpperCamelCase      :	List[str]				       =     timestep.to(self.timesteps.device				)
							_UpperCamelCase      :	Optional[Any]				       =     (self.timesteps == timestep).nonzero().item()
							_UpperCamelCase      :	Any				       =     self.sigmas[step_index]
							_UpperCamelCase      :	Dict				       =     sample / ((sigma**2 + 1) ** 0.5)
							_UpperCamelCase      :	Optional[Any]				       =     True
							return sample





	def 			UpperCamelCase_						(				self      :       List[Any]				,lowerCamelCase__      :       Optional[int]				,lowerCamelCase__      :       int				,lowerCamelCase__      :       Optional[Any]				):







							'''simple docstring'''

							def lms_derivative(lowerCamelCase__      :       str				):
													_UpperCamelCase      :	Any				       =     1.0
													for k in range(lowerCamelCase__				):
																			if current_order == k:
																									continue
																			prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
													return prod

							_UpperCamelCase      :	Union[str, Any]				       =     integrate.quad(lowerCamelCase__				,self.sigmas[t]				,self.sigmas[t + 1]				,epsrel=1E-4				)[0]

							return integrated_coeff





	def 			UpperCamelCase_						(				self      :       Dict				,lowerCamelCase__      :       int				,lowerCamelCase__      :       Union[str, torch.device] = None				):







							'''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      :	int				       =     np.linspace(0				,self.config.num_train_timesteps - 1				,lowerCamelCase__				,dtype=lowerCamelCase__				)[
													    ::-1
													].copy()
							elif self.config.timestep_spacing == "leading":
													_UpperCamelCase      :	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
													_UpperCamelCase      :	str				       =     (np.arange(0				,lowerCamelCase__				) * step_ratio).round()[::-1].copy().astype(lowerCamelCase__				)
													timesteps += self.config.steps_offset
							elif self.config.timestep_spacing == "trailing":
													_UpperCamelCase      :	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
													_UpperCamelCase      :	Optional[Any]				       =     (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      :	Optional[Any]				       =     np.log(lowerCamelCase__				)
							_UpperCamelCase      :	Dict				       =     np.interp(lowerCamelCase__				,np.arange(0				,len(lowerCamelCase__				)				)				,lowerCamelCase__				)

							if self.use_karras_sigmas:
													_UpperCamelCase      :	Optional[int]				       =     self._convert_to_karras(in_sigmas=lowerCamelCase__				)
													_UpperCamelCase      :	str				       =     np.array([self._sigma_to_t(lowerCamelCase__				,lowerCamelCase__				) for sigma in sigmas]				)

							_UpperCamelCase      :	List[str]				       =     np.concatenate([sigmas, [0.0]]				).astype(np.floataa				)

							_UpperCamelCase      :	Any				       =     torch.from_numpy(lowerCamelCase__				).to(device=lowerCamelCase__				)
							if str(lowerCamelCase__				).startswith('mps'				):
													# mps does not support float64
													_UpperCamelCase      :	Optional[Any]				       =     torch.from_numpy(lowerCamelCase__				).to(lowerCamelCase__				,dtype=torch.floataa				)
							else:
													_UpperCamelCase      :	Any				       =     torch.from_numpy(lowerCamelCase__				).to(device=lowerCamelCase__				)

							_UpperCamelCase      :	Union[str, Any]				       =     []





	def 			UpperCamelCase_						(				self      :       Any				,lowerCamelCase__      :       Any				,lowerCamelCase__      :       List[str]				):







							'''simple docstring'''
							# get log sigma
							_UpperCamelCase      :	Tuple				       =     np.log(lowerCamelCase__				)

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

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

							_UpperCamelCase      :	Optional[int]				       =     log_sigmas[low_idx]
							_UpperCamelCase      :	Union[str, Any]				       =     log_sigmas[high_idx]

							# interpolate sigmas
							_UpperCamelCase      :	List[Any]				       =     (low - log_sigma) / (low - high)
							_UpperCamelCase      :	int				       =     np.clip(lowerCamelCase__				,0				,1				)

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





	def 			UpperCamelCase_						(				self      :       Optional[Any]				,lowerCamelCase__      :       torch.FloatTensor				):







							'''simple docstring'''
							_UpperCamelCase      :	float				       =     in_sigmas[-1].item()
							_UpperCamelCase      :	float				       =     in_sigmas[0].item()

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





	def 			UpperCamelCase_						(				self      :       Optional[Any]				,lowerCamelCase__      :       torch.FloatTensor				,lowerCamelCase__      :       Union[float, torch.FloatTensor]				,lowerCamelCase__      :       torch.FloatTensor				,lowerCamelCase__      :       int = 4				,lowerCamelCase__      :       bool = True				,):







							'''simple docstring'''
							if not self.is_scale_input_called:
													warnings.warn(
													    '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      :	Union[str, Any]				       =     timestep.to(self.timesteps.device				)
							_UpperCamelCase      :	Any				       =     (self.timesteps == timestep).nonzero().item()
							_UpperCamelCase      :	Optional[int]				       =     self.sigmas[step_index]

							# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
							if self.config.prediction_type == "epsilon":
													_UpperCamelCase      :	Dict				       =     sample - sigma * model_output
							elif self.config.prediction_type == "v_prediction":
													# * c_out + input * c_skip
													_UpperCamelCase      :	str				       =     model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
							elif self.config.prediction_type == "sample":
													_UpperCamelCase      :	Any				       =     model_output
							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      :	List[Any]				       =     (sample - pred_original_sample) / sigma
							self.derivatives.append(lowerCamelCase__				)
							if len(self.derivatives				) > order:
													self.derivatives.pop(0				)

							# 3. Compute linear multistep coefficients
							_UpperCamelCase      :	List[Any]				       =     min(step_index + 1				,lowerCamelCase__				)
							_UpperCamelCase      :	Optional[int]				       =     [self.get_lms_coefficient(lowerCamelCase__				,lowerCamelCase__				,lowerCamelCase__				) for curr_order in range(lowerCamelCase__				)]

							# 4. Compute previous sample based on the derivatives path
							_UpperCamelCase      :	int				       =     sample + sum(
							    coeff * derivative for coeff, derivative in zip(lowerCamelCase__				,reversed(self.derivatives				)				)				)

							if not return_dict:
													return (prev_sample,)

							return LMSDiscreteSchedulerOutput(prev_sample=lowerCamelCase__				,pred_original_sample=lowerCamelCase__				)





	def 			UpperCamelCase_						(				self      :       Optional[Any]				,lowerCamelCase__      :       torch.FloatTensor				,lowerCamelCase__      :       torch.FloatTensor				,lowerCamelCase__      :       torch.FloatTensor				,):







							'''simple docstring'''
							# Make sure sigmas and timesteps have the same device and dtype as original_samples
							_UpperCamelCase      :	Tuple				       =     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      :	str				       =     self.timesteps.to(original_samples.device				,dtype=torch.floataa				)
													_UpperCamelCase      :	Optional[Any]				       =     timesteps.to(original_samples.device				,dtype=torch.floataa				)
							else:
													_UpperCamelCase      :	Union[str, Any]				       =     self.timesteps.to(original_samples.device				)
													_UpperCamelCase      :	Union[str, Any]				       =     timesteps.to(original_samples.device				)

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

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

							_UpperCamelCase      :	str				       =     original_samples + noise * sigma
							return noisy_samples





	def __len__(				self      :       List[Any]				):







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


