





"""simple docstring"""





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   (_SCREAMING_SNAKE_CASE     ,   _SCREAMING_SNAKE_CASE=BITS			)					->List[str]:





  """simple docstring"""


  lowerCAmelCase__			:Any											=							x.device

  lowerCAmelCase__			:Optional[int]											=							(x * 255).int().clamp(0     ,   255			)

  lowerCAmelCase__			:str											=							2 ** torch.arange(bits - 1     ,   -1     ,   -1     ,   device=A_			)
  lowerCAmelCase__			:List[Any]											=							rearrange(A_     ,   'd -> d 1 1'			)
  lowerCAmelCase__			:Any											=							rearrange(A_     ,   'b c h w -> b c 1 h w'			)

  lowerCAmelCase__			:Dict											=							((x & mask) != 0).float()
  lowerCAmelCase__			:Any											=							rearrange(A_     ,   'b c d h w -> b (c d) h w'			)
  lowerCAmelCase__			:Union[str, Any]											=							bits * 2 - 1
  return bits
def  __A   (_SCREAMING_SNAKE_CASE     ,   _SCREAMING_SNAKE_CASE=BITS			)					->Optional[int]:





  """simple docstring"""


  lowerCAmelCase__			:str											=							x.device

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

  lowerCAmelCase__			:Dict											=							rearrange(A_     ,   'd -> d 1 1'			)
  lowerCAmelCase__			:List[str]											=							rearrange(A_     ,   'b (c d) h w -> b c d h w'     ,   d=8			)
  lowerCAmelCase__			:Union[str, Any]											=							reduce(x * mask     ,   'b c d h w -> b c h w'     ,   'sum'			)
  return (dec / 255).clamp(0.0     ,   1.0			)
def  __A   (self     ,   _SCREAMING_SNAKE_CASE     ,   _SCREAMING_SNAKE_CASE     ,   _SCREAMING_SNAKE_CASE     ,   _SCREAMING_SNAKE_CASE = 0.0     ,   _SCREAMING_SNAKE_CASE = True     ,   _SCREAMING_SNAKE_CASE=None     ,   _SCREAMING_SNAKE_CASE = True     ,   )					->Optional[int]:





  """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)
  lowerCAmelCase__			:int											=							timestep - self.config.num_train_timesteps // self.num_inference_steps

  # 2. compute alphas, betas
  lowerCAmelCase__			:Tuple											=							self.alphas_cumprod[timestep]
  lowerCAmelCase__			:Dict											=							self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod

  lowerCAmelCase__			:Any											=							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
  lowerCAmelCase__			:Union[str, Any]											=							(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5

  # 4. Clip "predicted x_0"
  lowerCAmelCase__			:str											=							self.bit_scale
  if self.config.clip_sample:
    lowerCAmelCase__			:Dict											=							torch.clamp(A_     ,   -scale     ,   A_			)

  # 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)
  lowerCAmelCase__			:str											=							self._get_variance(A_     ,   A_			)
  lowerCAmelCase__			:List[Any]											=							eta * variance ** 0.5

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

    lowerCAmelCase__			:Optional[int]											=							prev_sample + variance

  if not return_dict:
    return (prev_sample,)

  return DDIMSchedulerOutput(prev_sample=A_     ,   pred_original_sample=A_			)
def  __A   (self     ,   _SCREAMING_SNAKE_CASE     ,   _SCREAMING_SNAKE_CASE     ,   _SCREAMING_SNAKE_CASE     ,   _SCREAMING_SNAKE_CASE="epsilon"     ,   _SCREAMING_SNAKE_CASE=None     ,   _SCREAMING_SNAKE_CASE = True     ,   )					->str:





  """simple docstring"""


  lowerCAmelCase__			:Union[str, Any]											=							timestep

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

  # 1. compute alphas, betas
  lowerCAmelCase__			:List[str]											=							self.alphas_cumprod[t]
  lowerCAmelCase__			:Tuple											=							self.alphas_cumprod[t - 1] if t > 0 else self.one
  lowerCAmelCase__			:List[str]											=							1 - alpha_prod_t
  lowerCAmelCase__			:List[Any]											=							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":
    lowerCAmelCase__			:Optional[int]											=							(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
  elif prediction_type == "sample":
    lowerCAmelCase__			:Any											=							model_output
  else:
    raise ValueError(F"Unsupported prediction_type {prediction_type}."			)

  # 3. Clip "predicted x_0"
  lowerCAmelCase__			:List[Any]											=							self.bit_scale
  if self.config.clip_sample:
    lowerCAmelCase__			:Dict											=							torch.clamp(A_     ,   -scale     ,   A_			)

  # 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
  lowerCAmelCase__			:Optional[int]											=							(alpha_prod_t_prev ** 0.5 * self.betas[t]) / beta_prod_t
  lowerCAmelCase__			:int											=							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
  lowerCAmelCase__			:Optional[Any]											=							pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

  # 6. Add noise
  lowerCAmelCase__			:int											=							0
  if t > 0:
    lowerCAmelCase__			:Optional[Any]											=							torch.randn(
        model_output.size()     ,   dtype=model_output.dtype     ,   layout=model_output.layout     ,   generator=A_			).to(model_output.device			)
    lowerCAmelCase__			:Union[str, Any]											=							(self._get_variance(A_     ,   predicted_variance=A_			) ** 0.5) * noise

  lowerCAmelCase__			:Any											=							pred_prev_sample + variance

  if not return_dict:
    return (pred_prev_sample,)

  return DDPMSchedulerOutput(prev_sample=A_     ,   pred_original_sample=A_			)






class 					_lowerCAmelCase   (     a_       ):
       """simple docstring"""




       def __init__(    self    , __UpperCAmelCase    , __UpperCAmelCase    , __UpperCAmelCase = 1.0    , ):



         '''simple docstring'''

         super().__init__()
         lowerCAmelCase__			:Any											=							bit_scale
         lowerCAmelCase__			:Optional[int]											=							(
             ddim_bit_scheduler_step if isinstance(lowercase_    , lowercase_      ) else ddpm_bit_scheduler_step
         )

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






       @torch.no_grad()
       def __call__(    self    , __UpperCAmelCase = 2_5_6    , __UpperCAmelCase = 2_5_6    , __UpperCAmelCase = 5_0    , __UpperCAmelCase = None    , __UpperCAmelCase = 1    , __UpperCAmelCase = "pil"    , __UpperCAmelCase = True    , **__UpperCAmelCase    , ):



         '''simple docstring'''

         lowerCAmelCase__			:List[Any]											=							torch.randn(
             (batch_size, self.unet.config.in_channels, height, width)    , generator=lowercase_    , )
         lowerCAmelCase__			:int											=							decimal_to_bits(lowercase_      ) * self.bit_scale
         lowerCAmelCase__			:Optional[int]											=							latents.to(self.device      )

         self.scheduler.set_timesteps(lowercase_      )

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

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

         lowerCAmelCase__			:Optional[Any]											=							bits_to_decimal(lowercase_      )

         if output_type == "pil":
           lowerCAmelCase__			:Union[str, Any]											=							self.numpy_to_pil(lowercase_      )

         if not return_dict:
           return (image,)

         return ImagePipelineOutput(images=lowercase_      )



"""simple docstring"""





import random

def   __SCREAMING_SNAKE_CASE  (      A_						,     A_ ):
	lowerCAmelCase__				,lowerCAmelCase__				,lowerCAmelCase__	:						Optional[int]  				=	[], [], []
	for element in data:
		if element < pivot:
			less.append(A_ )
		elif element > pivot:
			greater.append(A_ )
		else:
			equal.append(A_ )
	return less, equal, greater





def   __SCREAMING_SNAKE_CASE  (      A_						,     A_ ):
	# index = len(items) // 2 when trying to find the median
	#   (value of index when items is sorted)

	# invalid input
	if index >= len(A_ ) or index < 0:
		return None

	lowerCAmelCase__	:						str  				=	items[random.randint(0						,     len(A_ ) - 1 )]
	lowerCAmelCase__	:						Optional[Any]  				=	0
	lowerCAmelCase__				,lowerCAmelCase__				,lowerCAmelCase__	:						Any  				=	_partition(A_						,     A_ )
	lowerCAmelCase__	:						str  				=	len(A_ )
	lowerCAmelCase__	:						Optional[Any]  				=	len(A_ )

	# index is the pivot
	if m <= index < m + count:
		return pivot
	# must be in smaller
	elif m > index:
		return quick_select(A_						,     A_ )
	# must be in larger
	else:
		return quick_select(A_						,     index - (m + count) )




