






'''simple docstring'''





def      __lowercase					( snake_case,  snake_case,  snake_case ):







				"""simple docstring"""






				__magic_name__		:str        =      (num_of_terms / 2) * (2 * first_term + (num_of_terms - 1) * common_diff)
				# formula for sum of series
				return total

def      __lowercase					( ):







				"""simple docstring"""






				print(sum_of_series(1,  1,  1_0 ) )


if __name__ == "__main__":
					import doctest

					doctest.testmod()














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


SCREAMING_SNAKE_CASE__      :			Any							=		8

def      __lowercase					( snake_case,  snake_case=BITS ):







				"""simple docstring"""






				__magic_name__		:int        =      x.device

				__magic_name__		:Optional[Any]        =      (x * 2_5_5).int().clamp(0,  2_5_5 )

				__magic_name__		:Dict        =      2 ** torch.arange(bits - 1,  -1,  -1,  device=snake_case )
				__magic_name__		:Any        =      rearrange(snake_case,  '''d -> d 1 1''' )
				__magic_name__		:Dict        =      rearrange(snake_case,  '''b c h w -> b c 1 h w''' )

				__magic_name__		:Optional[Any]        =      ((x & mask) != 0).float()
				__magic_name__		:List[str]        =      rearrange(snake_case,  '''b c d h w -> b (c d) h w''' )
				__magic_name__		:List[Any]        =      bits * 2 - 1
				return bits

def      __lowercase					( snake_case,  snake_case=BITS ):







				"""simple docstring"""






				__magic_name__		:Optional[int]        =      x.device

				__magic_name__		:Dict        =      (x > 0).int()
				__magic_name__		:int        =      2 ** torch.arange(bits - 1,  -1,  -1,  device=snake_case,  dtype=torch.intaa )

				__magic_name__		:Optional[Any]        =      rearrange(snake_case,  '''d -> d 1 1''' )
				__magic_name__		:Union[str, Any]        =      rearrange(snake_case,  '''b (c d) h w -> b c d h w''',  d=8 )
				__magic_name__		:Optional[Any]        =      reduce(x * mask,  '''b c d h w -> b c h w''',  '''sum''' )
				return (dec / 2_5_5).clamp(0.0,  1.0 )

def      __lowercase					( self,  snake_case,  snake_case,  snake_case,  snake_case = 0.0,  snake_case = True,  snake_case=None,  snake_case = 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)
				__magic_name__		:Union[str, Any]        =      timestep - self.config.num_train_timesteps // self.num_inference_steps

				# 2. compute alphas, betas
				__magic_name__		:Optional[Any]        =      self.alphas_cumprod[timestep]
				__magic_name__		:List[Any]        =      self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod

				__magic_name__		:Dict        =      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
				__magic_name__		:List[Any]        =      (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5

				# 4. Clip "predicted x_0"
				__magic_name__		:Optional[int]        =      self.bit_scale
				if self.config.clip_sample:
								__magic_name__		:Dict        =      torch.clamp(snake_case,  -scale,  snake_case )

				# 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)
				__magic_name__		:Optional[Any]        =      self._get_variance(snake_case,  snake_case )
				__magic_name__		:Tuple        =      eta * variance ** 0.5

				if use_clipped_model_output:
								# the model_output is always re-derived from the clipped x_0 in Glide
								__magic_name__		:int        =      (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
				__magic_name__		:Tuple        =      (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
				__magic_name__		:str        =      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
								__magic_name__		:List[str]        =      model_output.device if torch.is_tensor(snake_case ) else '''cpu'''
								__magic_name__		:Tuple        =      torch.randn(model_output.shape,  dtype=model_output.dtype,  generator=snake_case ).to(snake_case )
								__magic_name__		:Optional[Any]        =      self._get_variance(snake_case,  snake_case ) ** 0.5 * eta * noise

								__magic_name__		:List[Any]        =      prev_sample + variance

				if not return_dict:
								return (prev_sample,)

				return DDIMSchedulerOutput(prev_sample=snake_case,  pred_original_sample=snake_case )

def      __lowercase					( self,  snake_case,  snake_case,  snake_case,  snake_case="epsilon",  snake_case=None,  snake_case = True,  ):







				"""simple docstring"""






				__magic_name__		:int        =      timestep

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

				# 1. compute alphas, betas
				__magic_name__		:List[str]        =      self.alphas_cumprod[t]
				__magic_name__		:List[str]        =      self.alphas_cumprod[t - 1] if t > 0 else self.one
				__magic_name__		:Any        =      1 - alpha_prod_t
				__magic_name__		:Tuple        =      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":
								__magic_name__		:str        =      (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
				elif prediction_type == "sample":
								__magic_name__		:List[Any]        =      model_output
				else:
								raise ValueError(f'''Unsupported prediction_type {prediction_type}.''' )

				# 3. Clip "predicted x_0"
				__magic_name__		:List[str]        =      self.bit_scale
				if self.config.clip_sample:
								__magic_name__		:int        =      torch.clamp(snake_case,  -scale,  snake_case )

				# 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
				__magic_name__		:Any        =      (alpha_prod_t_prev ** 0.5 * self.betas[t]) / beta_prod_t
				__magic_name__		:str        =      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
				__magic_name__		:List[Any]        =      pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

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

				__magic_name__		:int        =      pred_prev_sample + variance

				if not return_dict:
								return (pred_prev_sample,)

				return DDPMSchedulerOutput(prev_sample=snake_case,  pred_original_sample=snake_case )

class 						lowerCamelCase_				(      lowerCamelCase ):







				def __init__(						self       ,					__lowerCAmelCase       ,					__lowerCAmelCase       ,					__lowerCAmelCase = 1.0       ,					):
								"""simple docstring"""
								super().__init__()
								__magic_name__		:Any        =      bit_scale
								__magic_name__		:List[Any]        =      (
								    ddim_bit_scheduler_step if isinstance(__lowerCAmelCase       ,					__lowerCAmelCase     ) else ddpm_bit_scheduler_step
								)

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







				@torch.no_grad()
				def __call__(						self       ,					__lowerCAmelCase = 2_5_6       ,					__lowerCAmelCase = 2_5_6       ,					__lowerCAmelCase = 5_0       ,					__lowerCAmelCase = None       ,					__lowerCAmelCase = 1       ,					__lowerCAmelCase = "pil"       ,					__lowerCAmelCase = True       ,					**__lowerCAmelCase       ,					):
								"""simple docstring"""
								__magic_name__		:List[str]        =      torch.randn(
								    (batch_size, self.unet.config.in_channels, height, width)       ,					generator=__lowerCAmelCase       ,					)
								__magic_name__		:List[str]        =      decimal_to_bits(__lowerCAmelCase     ) * self.bit_scale
								__magic_name__		:int        =      latents.to(self.device     )

								self.scheduler.set_timesteps(__lowerCAmelCase     )

								for t in self.progress_bar(self.scheduler.timesteps     ):
												# predict the noise residual
												__magic_name__		:List[Any]        =      self.unet(__lowerCAmelCase       ,					__lowerCAmelCase     ).sample

												# compute the previous noisy sample x_t -> x_t-1
												__magic_name__		:Any        =      self.scheduler.step(__lowerCAmelCase       ,					__lowerCAmelCase       ,					__lowerCAmelCase     ).prev_sample

								__magic_name__		:str        =      bits_to_decimal(__lowerCAmelCase     )

								if output_type == "pil":
												__magic_name__		:Any        =      self.numpy_to_pil(__lowerCAmelCase     )

								if not return_dict:
												return (image,)

								return ImagePipelineOutput(images=__lowerCAmelCase     )






