



'''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


_UpperCamelCase											=						8

def        a_     (							_lowerCAmelCase       ,_lowerCAmelCase=BITS       )      ->      Any:
  __lowerCamelCase       :       List[str]           = x.device

  __lowerCamelCase       :       int           = (x * 255).int().clamp(0       ,255       )

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

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

def        a_     (							_lowerCAmelCase       ,_lowerCAmelCase=BITS       )      ->      Optional[Any]:
  __lowerCamelCase       :       int           = x.device

  __lowerCamelCase       :       int           = (x > 0).int()
  __lowerCamelCase       :       List[str]           = 2 ** torch.arange(bits - 1       ,-1       ,-1       ,device=_lowerCAmelCase       ,dtype=torch.intaa       )

  __lowerCamelCase       :       Any           = rearrange(_lowerCAmelCase       ,'d -> d 1 1'       )
  __lowerCamelCase       :       Any           = rearrange(_lowerCAmelCase       ,'b (c d) h w -> b c d h w'       ,d=8       )
  __lowerCamelCase       :       List[str]           = reduce(x * mask       ,'b c d h w -> b c h w'       ,'sum'       )
  return (dec / 255).clamp(0.0       ,1.0       )

def        a_     (							self       ,_lowerCAmelCase       ,_lowerCAmelCase       ,_lowerCAmelCase       ,_lowerCAmelCase = 0.0       ,_lowerCAmelCase = True       ,_lowerCAmelCase=None       ,_lowerCAmelCase = True       ,)      ->      Union[DDIMSchedulerOutput, Tuple]:
  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       :       Optional[Any]           = timestep - self.config.num_train_timesteps // self.num_inference_steps

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

  __lowerCamelCase       :       Union[str, 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       :       Optional[int]           = (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5

  # 4. Clip "predicted x_0"
  __lowerCamelCase       :       Dict           = self.bit_scale
  if self.config.clip_sample:
    __lowerCamelCase       :       Optional[Any]           = 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)
  __lowerCamelCase       :       int           = self._get_variance(_lowerCAmelCase       ,_lowerCAmelCase       )
  __lowerCamelCase       :       Tuple           = eta * variance ** 0.5

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

    __lowerCamelCase       :       int           = prev_sample + variance

  if not return_dict:
    return (prev_sample,)

  return DDIMSchedulerOutput(prev_sample=_lowerCAmelCase       ,pred_original_sample=_lowerCAmelCase       )

def        a_     (							self       ,_lowerCAmelCase       ,_lowerCAmelCase       ,_lowerCAmelCase       ,_lowerCAmelCase="epsilon"       ,_lowerCAmelCase=None       ,_lowerCAmelCase = True       ,)      ->      Union[DDPMSchedulerOutput, Tuple]:
  __lowerCamelCase       :       Dict           = timestep

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

  # 1. compute alphas, betas
  __lowerCamelCase       :       Optional[int]           = self.alphas_cumprod[t]
  __lowerCamelCase       :       Optional[int]           = self.alphas_cumprod[t - 1] if t > 0 else self.one
  __lowerCamelCase       :       Any           = 1 - alpha_prod_t
  __lowerCamelCase       :       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       :       List[Any]           = (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       :       Optional[Any]           = self.bit_scale
  if self.config.clip_sample:
    __lowerCamelCase       :       Union[str, Any]           = 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
  __lowerCamelCase       :       Union[str, Any]           = (alpha_prod_t_prev ** 0.5 * self.betas[t]) / beta_prod_t
  __lowerCamelCase       :       Dict           = 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       :       Dict           = pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

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

  __lowerCamelCase       :       str           = pred_prev_sample + variance

  if not return_dict:
    return (pred_prev_sample,)

  return DDPMSchedulerOutput(prev_sample=_lowerCAmelCase       ,pred_original_sample=_lowerCAmelCase       )






class 					lowerCamelCase_    (				SCREAMING_SNAKE_CASE_     ):
  """simple docstring"""




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

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




  @torch.no_grad()
  def __call__( self      :	Tuple			,	_a      :	Optional[int] = 256			,	_a      :	Optional[int] = 256			,	_a      :	Optional[int] = 50			,	_a      :	Optional[torch.Generator] = None			,	_a      :	Optional[int] = 1			,	_a      :	Optional[str] = "pil"			,	_a      :	bool = True			,	**_a      :	Dict			,	)					->					Union[Tuple, ImagePipelineOutput]:
    __lowerCamelCase       :       str           = torch.randn(
        (batch_size, self.unet.config.in_channels, height, width)			,	generator=_a			,	)
    __lowerCamelCase       :       int           = decimal_to_bits(_a   ) * self.bit_scale
    __lowerCamelCase       :       Dict           = latents.to(self.device   )

    self.scheduler.set_timesteps(_a   )

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

      # compute the previous noisy sample x_t -> x_t-1
      __lowerCamelCase       :       List[Any]           = self.scheduler.step(_a			,	_a			,	_a   ).prev_sample

    __lowerCamelCase       :       Dict           = bits_to_decimal(_a   )

    if output_type == "pil":
      __lowerCamelCase       :       int           = self.numpy_to_pil(_a   )

    if not return_dict:
      return (image,)

    return ImagePipelineOutput(images=_a   )











'''simple docstring'''





from __future__ import annotations

import math
from collections.abc import Callable

def        a_     (							_lowerCAmelCase       ,_lowerCAmelCase       ,_lowerCAmelCase       ,_lowerCAmelCase = 100       ,)      ->      float:
  __lowerCamelCase       :       Dict           = x_start
  __lowerCamelCase       :       int           = fnc(_lowerCAmelCase       )
  __lowerCamelCase       :       Dict           = 0.0

  for _ in range(_lowerCAmelCase       ):
    # Approximates curve as a sequence of linear lines and sums their length
    __lowerCamelCase       :       List[str]           = (x_end - x_start) / steps + xa
    __lowerCamelCase       :       List[Any]           = fnc(_lowerCAmelCase       )
    length += math.hypot(xa - xa       ,fxa - fxa       )

    # Increment step
    __lowerCamelCase       :       Any           = xa
    __lowerCamelCase       :       Tuple           = fxa

  return length


if __name__ == "__main__":

   def        a_     (							_lowerCAmelCase       )      ->      Dict:
     return math.sin(10 * x       )

   print('f(x) = sin(10 * x)')
   print('The length of the curve from x = -10 to x = 10 is:')
   _UpperCamelCase											=						10
   while i <= 100000:
      print(f'''With {i} steps: {line_length(f, -10, 10, i)}''')
      i *= 10






