
from typing import Optional, Tuple, Union

import torch
from einops import rearrange, reduce

from diffusers import DDIMScheduler, DDPMScheduler, DiffusionPipeline, ImagePipelineOutput, UNetaDConditionModel
from diffusers.schedulers.scheduling_ddim import DDIMSchedulerOutput
from diffusers.schedulers.scheduling_ddpm import DDPMSchedulerOutput


__a  			=					8




def 				a						(							snake_case__:					Optional[int]						,   snake_case__:					Union[str, Any]=BITS					):


				'''simple docstring'''
				lowercase_       =					x.device

				lowercase_       =					(x * 255).int().clamp(0						,   255					)

				lowercase_       =					2 ** torch.arange(bits - 1						,   -1						,   -1						,   device=__lowerCAmelCase					)
				lowercase_       =					rearrange(__lowerCAmelCase						,   '''d -> d 1 1'''					)
				lowercase_       =					rearrange(__lowerCAmelCase						,   '''b c h w -> b c 1 h w'''					)

				lowercase_       =					((x & mask) != 0).float()
				lowercase_       =					rearrange(__lowerCAmelCase						,   '''b c d h w -> b (c d) h w'''					)
				lowercase_       =					bits * 2 - 1
				return bits




def 				a						(							snake_case__:					int						,   snake_case__:					Optional[Any]=BITS					):


				'''simple docstring'''
				lowercase_       =					x.device

				lowercase_       =					(x > 0).int()
				lowercase_       =					2 ** torch.arange(bits - 1						,   -1						,   -1						,   device=__lowerCAmelCase						,   dtype=torch.intaa					)

				lowercase_       =					rearrange(__lowerCAmelCase						,   '''d -> d 1 1'''					)
				lowercase_       =					rearrange(__lowerCAmelCase						,   '''b (c d) h w -> b c d h w'''						,   d=8					)
				lowercase_       =					reduce(x * mask						,   '''b c d h w -> b c h w'''						,   '''sum'''					)
				return (dec / 255).clamp(0.0						,   1.0					)




def 				a						(							self:					str						,   snake_case__:					torch.FloatTensor						,   snake_case__:					int						,   snake_case__:					torch.FloatTensor						,   snake_case__:					float = 0.0						,   snake_case__:					bool = True						,   snake_case__:					Any=None						,   snake_case__:					bool = True						,   ):


				'''simple docstring'''
				if self.num_inference_steps is None:
								raise ValueError(
								    '''Number of inference steps is \'None\', you need to run \'set_timesteps\' after creating the scheduler'''					)

				# See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf
				# Ideally, read DDIM paper in-detail understanding

				# Notation (<variable name> -> <name in paper>
				# - pred_noise_t -> e_theta(x_t, t)
				# - pred_original_sample -> f_theta(x_t, t) or x_0
				# - std_dev_t -> sigma_t
				# - eta -> η
				# - pred_sample_direction -> "direction pointing to x_t"
				# - pred_prev_sample -> "x_t-1"

				# 1. get previous step value (=t-1)
				lowercase_       =					timestep - self.config.num_train_timesteps // self.num_inference_steps

				# 2. compute alphas, betas
				lowercase_       =					self.alphas_cumprod[timestep]
				lowercase_       =					self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod

				lowercase_       =					1 - alpha_prod_t

				# 3. compute predicted original sample from predicted noise also called
				# "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
				lowercase_       =					(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5

				# 4. Clip "predicted x_0"
				lowercase_       =					self.bit_scale
				if self.config.clip_sample:
								lowercase_       =					torch.clamp(__lowerCAmelCase						,   -scale						,   __lowerCAmelCase					)

				# 5. compute variance: "sigma_t(η)" -> see formula (16)
				# σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1)
				lowercase_       =					self._get_variance(__lowerCAmelCase						,   __lowerCAmelCase					)
				lowercase_       =					eta * variance ** 0.5

				if use_clipped_model_output:
								# the model_output is always re-derived from the clipped x_0 in Glide
								lowercase_       =					(sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5

				# 6. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
				lowercase_       =					(1 - alpha_prod_t_prev - std_dev_t**2) ** 0.5 * model_output

				# 7. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
				lowercase_       =					alpha_prod_t_prev ** 0.5 * pred_original_sample + pred_sample_direction

				if eta > 0:
								# randn_like does not support generator https://github.com/pytorch/pytorch/issues/27072
								lowercase_       =					model_output.device if torch.is_tensor(__lowerCAmelCase					) else '''cpu'''
								lowercase_       =					torch.randn(model_output.shape						,   dtype=model_output.dtype						,   generator=__lowerCAmelCase					).to(__lowerCAmelCase					)
								lowercase_       =					self._get_variance(__lowerCAmelCase						,   __lowerCAmelCase					) ** 0.5 * eta * noise

								lowercase_       =					prev_sample + variance

				if not return_dict:
								return (prev_sample,)

				return DDIMSchedulerOutput(prev_sample=__lowerCAmelCase						,   pred_original_sample=__lowerCAmelCase					)




def 				a						(							self:					int						,   snake_case__:					torch.FloatTensor						,   snake_case__:					int						,   snake_case__:					torch.FloatTensor						,   snake_case__:					Dict="epsilon"						,   snake_case__:					Dict=None						,   snake_case__:					bool = True						,   ):


				'''simple docstring'''
				lowercase_       =					timestep

				if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type in ["learned", "learned_range"]:
								lowercase_  ,	lowercase_       =					torch.split(__lowerCAmelCase						,   sample.shape[1]						,   dim=1					)
				else:
								lowercase_       =					None

				# 1. compute alphas, betas
				lowercase_       =					self.alphas_cumprod[t]
				lowercase_       =					self.alphas_cumprod[t - 1] if t > 0 else self.one
				lowercase_       =					1 - alpha_prod_t
				lowercase_       =					1 - alpha_prod_t_prev

				# 2. compute predicted original sample from predicted noise also called
				# "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
				if prediction_type == "epsilon":
								lowercase_       =					(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
				elif prediction_type == "sample":
								lowercase_       =					model_output
				else:
								raise ValueError(F'''Unsupported prediction_type {prediction_type}.'''					)

				# 3. Clip "predicted x_0"
				lowercase_       =					self.bit_scale
				if self.config.clip_sample:
								lowercase_       =					torch.clamp(__lowerCAmelCase						,   -scale						,   __lowerCAmelCase					)

				# 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
				# See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
				lowercase_       =					(alpha_prod_t_prev ** 0.5 * self.betas[t]) / beta_prod_t
				lowercase_       =					self.alphas[t] ** 0.5 * beta_prod_t_prev / beta_prod_t

				# 5. Compute predicted previous sample µ_t
				# See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
				lowercase_       =					pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

				# 6. Add noise
				lowercase_       =					0
				if t > 0:
								lowercase_       =					torch.randn(
								    model_output.size()						,   dtype=model_output.dtype						,   layout=model_output.layout						,   generator=__lowerCAmelCase					).to(model_output.device					)
								lowercase_       =					(self._get_variance(__lowerCAmelCase						,   predicted_variance=__lowerCAmelCase					) ** 0.5) * noise

				lowercase_       =					pred_prev_sample + variance

				if not return_dict:
								return (pred_prev_sample,)

				return DDPMSchedulerOutput(prev_sample=__lowerCAmelCase						,   pred_original_sample=__lowerCAmelCase					)


class  lowercase__(				lowerCamelCase_							):



	"""simple docstring"""




	def __init__(       self  :			Union[str, Any]       ,							SCREAMING_SNAKE_CASE_  :			UNetaDConditionModel       ,							SCREAMING_SNAKE_CASE_  :			Union[DDIMScheduler, DDPMScheduler]       ,							SCREAMING_SNAKE_CASE_  :			Optional[float] = 1.0       ,							)       ->     Union[str, Any]:
					super().__init__()
					lowercase_       =					bit_scale
					lowercase_       =					(
					    ddim_bit_scheduler_step if isinstance(__snake_case       ,							__snake_case       ) else ddpm_bit_scheduler_step
					)

					self.register_modules(unet=__snake_case       ,							scheduler=__snake_case       )




	@torch.no_grad()
	def __call__(       self  :			Tuple       ,							SCREAMING_SNAKE_CASE_  :			Optional[int] = 2_5_6       ,							SCREAMING_SNAKE_CASE_  :			Optional[int] = 2_5_6       ,							SCREAMING_SNAKE_CASE_  :			Optional[int] = 5_0       ,							SCREAMING_SNAKE_CASE_  :			Optional[torch.Generator] = None       ,							SCREAMING_SNAKE_CASE_  :			Optional[int] = 1       ,							SCREAMING_SNAKE_CASE_  :			Optional[str] = "pil"       ,							SCREAMING_SNAKE_CASE_  :			bool = True       ,							**SCREAMING_SNAKE_CASE_  :			int       ,							)       ->     Union[Tuple, ImagePipelineOutput]:
					lowercase_       =					torch.randn(
					    (batch_size, self.unet.config.in_channels, height, width)       ,							generator=__snake_case       ,							)
					lowercase_       =					decimal_to_bits(__snake_case       ) * self.bit_scale
					lowercase_       =					latents.to(self.device       )

					self.scheduler.set_timesteps(__snake_case       )

					for t in self.progress_bar(self.scheduler.timesteps       ):
									# predict the noise residual
									lowercase_       =					self.unet(__snake_case       ,							__snake_case       ).sample

									# compute the previous noisy sample x_t -> x_t-1
									lowercase_       =					self.scheduler.step(__snake_case       ,							__snake_case       ,							__snake_case       ).prev_sample

					lowercase_       =					bits_to_decimal(__snake_case       )

					if output_type == "pil":
									lowercase_       =					self.numpy_to_pil(__snake_case       )

					if not return_dict:
									return (image,)

					return ImagePipelineOutput(images=__snake_case       )








def 							__lowercase   ( __lowerCAmelCase							:				list[int]   ):
							a__             =     []
							if len(__lowerCAmelCase   ) == 1:
														return [nums.copy()]
							for _ in range(len(__lowerCAmelCase   )   ):
														a__             =     nums.pop(0   )
														a__             =     permute(__lowerCAmelCase   )
														for perm in permutations:
																					perm.append(__lowerCAmelCase   )
														result.extend(__lowerCAmelCase   )
														nums.append(__lowerCAmelCase   )
							return result






def 							__lowercase   ( __lowerCAmelCase							:				Optional[int]   ):

							def backtrack(__lowerCAmelCase							:				Any   ):
														if start == len(__lowerCAmelCase   ) - 1:
																					output.append(nums[:]   )
														else:
																					for i in range(__lowerCAmelCase					,    len(__lowerCAmelCase   )   ):
																												a__      ,					a__             =     nums[i], nums[start]
																												backtrack(start + 1   )
																												a__      ,					a__             =     nums[i], nums[start]  # backtrack

							a__             =     []
							backtrack(0   )
							return output


if __name__ == "__main__":
						import doctest

						# use res to print the data in permute2 function
						snake_case							:       Optional[Any]     			=      permutea([1, 2, 3])
						print(res)
						doctest.testmod()




