




'''simple docstring'''





import math
from collections import defaultdict
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import randn_tensor
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput





def UpperCAmelCase    (       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}'''						)

    _a				:							Tuple							       =      []
    for i in range(UpperCAmelCase_						):
        _a				:							int							       =      i / num_diffusion_timesteps
        _a				:							List[str]							       =      (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      UpperCamelCase       (	snake_case__      ,		snake_case__       ):
  a     :Any          =					[e.name for e in KarrasDiffusionSchedulers]
  a     :List[Any]          =					2



  @register_to_config
  def __init__(			self		,     __lowerCAmelCase = 1000		,     __lowerCAmelCase = 0.00085		,     __lowerCAmelCase = 0.012		,     __lowerCAmelCase = "linear"		,     __lowerCAmelCase = None		,     __lowerCAmelCase = "epsilon"		,     __lowerCAmelCase = "linspace"		,     __lowerCAmelCase = 0		,     ):







      '''simple docstring'''


      if trained_betas is not None:
          _a				:							List[str]							       =      torch.tensor(__lowerCAmelCase		,     dtype=torch.floataa )
      elif beta_schedule == "linear":
          _a				:							Any							       =      torch.linspace(__lowerCAmelCase		,     __lowerCAmelCase		,     __lowerCAmelCase		,     dtype=torch.floataa )
      elif beta_schedule == "scaled_linear":
          # this schedule is very specific to the latent diffusion model.
          _a				:							Dict							       =      (
              torch.linspace(beta_start**0.5		,     beta_end**0.5		,     __lowerCAmelCase		,     dtype=torch.floataa ) ** 2
          )
      elif beta_schedule == "squaredcos_cap_v2":
          # Glide cosine schedule
          _a				:							int							       =      betas_for_alpha_bar(__lowerCAmelCase )
      else:
          raise NotImplementedError(f'''{beta_schedule} does is not implemented for {self.__class__}''' )

      _a				:							int							       =      1.0 - self.betas
      _a				:							Any							       =      torch.cumprod(self.alphas		,     dim=0 )

      #  set all values
      self.set_timesteps(__lowerCAmelCase		,     __lowerCAmelCase		,     __lowerCAmelCase )



  def     a_							(			self		,     __lowerCAmelCase		,     __lowerCAmelCase=None ):







      '''simple docstring'''


      if schedule_timesteps is None:
          _a				:							List[Any]							       =      self.timesteps

      _a				:							Tuple							       =      (schedule_timesteps == timestep).nonzero()

      # The sigma index that is taken for the **very** first `step`
      # is always the second index (or the last index if there is only 1)
      # This way we can ensure we don't accidentally skip a sigma in
      # case we start in the middle of the denoising schedule (e.g. for image-to-image)
      if len(self._index_counter ) == 0:
          _a				:							str							       =      1 if len(__lowerCAmelCase ) > 1 else 0
      else:
          _a				:							Optional[Any]							       =      timestep.cpu().item() if torch.is_tensor(__lowerCAmelCase ) else timestep
          _a				:							Any							       =      self._index_counter[timestep_int]

      return indices[pos].item()



  @property
  def     a_							(			self ):







      '''simple docstring'''


      if self.config.timestep_spacing in ["linspace", "trailing"]:
          return self.sigmas.max()

      return (self.sigmas.max() ** 2 + 1) ** 0.5



  def     a_							(			self		,     __lowerCAmelCase		,     __lowerCAmelCase		,     ):







      '''simple docstring'''


      _a				:							List[str]							       =      self.index_for_timestep(__lowerCAmelCase )

      if self.state_in_first_order:
          _a				:							Any							       =      self.sigmas[step_index]
      else:
          _a				:							Optional[int]							       =      self.sigmas_interpol[step_index - 1]

      _a				:							Optional[Any]							       =      sample / ((sigma**2 + 1) ** 0.5)
      return sample



  def     a_							(			self		,     __lowerCAmelCase		,     __lowerCAmelCase = None		,     __lowerCAmelCase = None		,     ):







      '''simple docstring'''


      _a				:							Any							       =      num_inference_steps

      _a				:							List[Any]							       =      num_train_timesteps or self.config.num_train_timesteps

      # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
      if self.config.timestep_spacing == "linspace":
          _a				:							Tuple							       =      np.linspace(0		,     num_train_timesteps - 1		,     __lowerCAmelCase		,     dtype=__lowerCAmelCase )[::-1].copy()
      elif self.config.timestep_spacing == "leading":
          _a				:							Any							       =      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
          _a				:							int							       =      (np.arange(0		,     __lowerCAmelCase ) * step_ratio).round()[::-1].copy().astype(__lowerCAmelCase )
          timesteps += self.config.steps_offset
      elif self.config.timestep_spacing == "trailing":
          _a				:							List[str]							       =      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
          _a				:							int							       =      (np.arange(__lowerCAmelCase		,     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\'.''' )

      _a				:							Dict							       =      np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5 )
      _a				:							Optional[Any]							       =      torch.from_numpy(np.log(__lowerCAmelCase ) ).to(__lowerCAmelCase )

      _a				:							List[Any]							       =      np.interp(__lowerCAmelCase		,     np.arange(0		,     len(__lowerCAmelCase ) )		,     __lowerCAmelCase )
      _a				:							Optional[Any]							       =      np.concatenate([sigmas, [0.0]] ).astype(np.floataa )
      _a				:							List[str]							       =      torch.from_numpy(__lowerCAmelCase ).to(device=__lowerCAmelCase )

      # compute up and down sigmas
      _a				:							Dict							       =      sigmas.roll(-1 )
      _a				:							Dict							       =      0.0
      _a				:							Optional[Any]							       =      (sigmas_next**2 * (sigmas**2 - sigmas_next**2) / sigmas**2) ** 0.5
      _a				:							Optional[Any]							       =      (sigmas_next**2 - sigmas_up**2) ** 0.5
      _a				:							Any							       =      0.0

      # compute interpolated sigmas
      _a				:							Any							       =      sigmas.log().lerp(sigmas_down.log()		,     0.5 ).exp()
      _a				:							Any							       =      0.0

      # set sigmas
      _a				:							Optional[Any]							       =      torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2 ), sigmas[-1:]] )
      _a				:							Optional[int]							       =      torch.cat(
          [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2 ), sigmas_interpol[-1:]] )
      _a				:							Tuple							       =      torch.cat([sigmas_up[:1], sigmas_up[1:].repeat_interleave(2 ), sigmas_up[-1:]] )
      _a				:							str							       =      torch.cat([sigmas_down[:1], sigmas_down[1:].repeat_interleave(2 ), sigmas_down[-1:]] )

      if str(__lowerCAmelCase ).startswith("""mps""" ):
          # mps does not support float64
          _a				:							int							       =      torch.from_numpy(__lowerCAmelCase ).to(__lowerCAmelCase		,     dtype=torch.floataa )
      else:
          _a				:							str							       =      torch.from_numpy(__lowerCAmelCase ).to(__lowerCAmelCase )

      _a				:							str							       =      self.sigma_to_t(__lowerCAmelCase ).to(__lowerCAmelCase		,     dtype=timesteps.dtype )
      _a				:							int							       =      torch.stack((timesteps_interpol[:-2, None], timesteps[1:, None])		,     dim=-1 ).flatten()

      _a				:							Optional[Any]							       =      torch.cat([timesteps[:1], interleaved_timesteps] )

      _a				:							Optional[int]							       =      None

      # for exp beta schedules, such as the one for `pipeline_shap_e.py`
      # we need an index counter
      _a				:							Any							       =      defaultdict(__lowerCAmelCase )



  def     a_							(			self		,     __lowerCAmelCase ):







      '''simple docstring'''


      _a				:							str							       =      sigma.log()

      # get distribution
      _a				:							Optional[Any]							       =      log_sigma - self.log_sigmas[:, None]

      # get sigmas range
      _a				:							Optional[int]							       =      dists.ge(0 ).cumsum(dim=0 ).argmax(dim=0 ).clamp(max=self.log_sigmas.shape[0] - 2 )
      _a				:							str							       =      low_idx + 1

      _a				:							Dict							       =      self.log_sigmas[low_idx]
      _a				:							Dict							       =      self.log_sigmas[high_idx]

      # interpolate sigmas
      _a				:							Dict							       =      (low - log_sigma) / (low - high)
      _a				:							Optional[int]							       =      w.clamp(0		,     1 )

      # transform interpolation to time range
      _a				:							Optional[Any]							       =      (1 - w) * low_idx + w * high_idx
      _a				:							int							       =      t.view(sigma.shape )
      return t



  @property
  def     a_							(			self ):







      '''simple docstring'''


      return self.sample is None



  def     a_							(			self		,     __lowerCAmelCase		,     __lowerCAmelCase		,     __lowerCAmelCase		,     __lowerCAmelCase = None		,     __lowerCAmelCase = True		,     ):







      '''simple docstring'''


      _a				:							str							       =      self.index_for_timestep(__lowerCAmelCase )

      # advance index counter by 1
      _a				:							Dict							       =      timestep.cpu().item() if torch.is_tensor(__lowerCAmelCase ) else timestep
      self._index_counter[timestep_int] += 1

      if self.state_in_first_order:
          _a				:							str							       =      self.sigmas[step_index]
          _a				:							List[str]							       =      self.sigmas_interpol[step_index]
          _a				:							Dict							       =      self.sigmas_up[step_index]
          _a				:							Any							       =      self.sigmas_down[step_index - 1]
      else:
          # 2nd order / KPDM2's method
          _a				:							Union[str, Any]							       =      self.sigmas[step_index - 1]
          _a				:							List[str]							       =      self.sigmas_interpol[step_index - 1]
          _a				:							Union[str, Any]							       =      self.sigmas_up[step_index - 1]
          _a				:							List[Any]							       =      self.sigmas_down[step_index - 1]

      # currently only gamma=0 is supported. This usually works best anyways.
      # We can support gamma in the future but then need to scale the timestep before
      # passing it to the model which requires a change in API
      _a				:							Any							       =      0
      _a				:							Tuple							       =      sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

      _a				:							Any							       =      model_output.device
      _a				:							Tuple							       =      randn_tensor(model_output.shape		,     dtype=model_output.dtype		,     device=__lowerCAmelCase		,     generator=__lowerCAmelCase )

      # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
      if self.config.prediction_type == "epsilon":
          _a				:							Dict							       =      sigma_hat if self.state_in_first_order else sigma_interpol
          _a				:							int							       =      sample - sigma_input * model_output
      elif self.config.prediction_type == "v_prediction":
          _a				:							Optional[int]							       =      sigma_hat if self.state_in_first_order else sigma_interpol
          _a				:							List[str]							       =      model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
              sample / (sigma_input**2 + 1)
          )
      elif self.config.prediction_type == "sample":
          raise NotImplementedError("""prediction_type not implemented yet: sample""" )
      else:
          raise ValueError(
              f'''prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`''' )

      if self.state_in_first_order:
          # 2. Convert to an ODE derivative for 1st order
          _a				:							Tuple							       =      (sample - pred_original_sample) / sigma_hat
          # 3. delta timestep
          _a				:							List[str]							       =      sigma_interpol - sigma_hat

          # store for 2nd order step
          _a				:							Optional[int]							       =      sample
          _a				:							str							       =      dt
          _a				:							Optional[int]							       =      sample + derivative * dt
      else:
          # DPM-Solver-2
          # 2. Convert to an ODE derivative for 2nd order
          _a				:							Any							       =      (sample - pred_original_sample) / sigma_interpol
          # 3. delta timestep
          _a				:							Union[str, Any]							       =      sigma_down - sigma_hat

          _a				:							Tuple							       =      self.sample
          _a				:							List[Any]							       =      None

          _a				:							Tuple							       =      sample + derivative * dt
          _a				:							int							       =      prev_sample + noise * sigma_up

      if not return_dict:
          return (prev_sample,)

      return SchedulerOutput(prev_sample=__lowerCAmelCase )



  def     a_							(			self		,     __lowerCAmelCase		,     __lowerCAmelCase		,     __lowerCAmelCase		,     ):







      '''simple docstring'''


      _a				:							List[Any]							       =      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
          _a				:							Union[str, Any]							       =      self.timesteps.to(original_samples.device		,     dtype=torch.floataa )
          _a				:							Optional[int]							       =      timesteps.to(original_samples.device		,     dtype=torch.floataa )
      else:
          _a				:							Optional[int]							       =      self.timesteps.to(original_samples.device )
          _a				:							str							       =      timesteps.to(original_samples.device )

      _a				:							str							       =      [self.index_for_timestep(__lowerCAmelCase		,     __lowerCAmelCase ) for t in timesteps]

      _a				:							str							       =      sigmas[step_indices].flatten()
      while len(sigma.shape ) < len(original_samples.shape ):
          _a				:							Union[str, Any]							       =      sigma.unsqueeze(-1 )

      _a				:							int							       =      original_samples + noise * sigma
      return noisy_samples



  def __len__(			self ):







      '''simple docstring'''


      return self.config.num_train_timesteps










"""simple docstring"""





from __future__ import annotations

from PIL import Image

# Define the first generation of cells
# fmt: off
UpperCamelCase_						:					int      				=			[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]



def      __lowercase       (     a			:					int			)       ->       list[int]:
      return [int(a			) for c in f'''{ruleset:08}'''[:8]]



def      __lowercase       (     a			:					list[list[int]]							,		a			:					list[int]							,		a			:					int			)       ->       list[int]:
      __snake_case   :     Optional[Any]	      =len(cells[0]			)  # 31
      __snake_case   :     List[str]	      =[]
      for i in range(a			):
            # Get the neighbors of each cell
            # Handle neighbours outside bounds by using 0 as their value
            __snake_case   :     Optional[Any]	      =0 if i == 0 else cells[time][i - 1]
            __snake_case   :     Dict	      =0 if i == population - 1 else cells[time][i + 1]
            # Define a new cell and add it to the new generation
            __snake_case   :     Optional[int]	      =7 - int(f'''{left_neighbor}{cells[time][i]}{right_neighbor}'''							,		2			)
            next_generation.append(rule[situation]			)
      return next_generation



def      __lowercase       (     a			:					list[list[int]]			)       ->       Image.Image:
      __snake_case   :     int	      =Image.new('''RGB'''							,		(len(cells[0]			), len(a			))			)
      __snake_case   :     List[Any]	      =img.load()
      # Generates image
      for w in range(img.width			):
            for h in range(img.height			):
                  __snake_case   :     int	      =255 - int(255 * cells[h][w]			)
                  __snake_case   :     List[str]	      =(color, color, color)
      return img


if __name__ == "__main__":
    UpperCamelCase_						:					Optional[Any]      				=			bin(int(input("""Rule:\n""").strip()))[2:]
    UpperCamelCase_						:					List[str]      				=			format_ruleset(int(rule_num))
    for time in range(16):
        CELLS.append(new_generation(CELLS, rule, time))
    UpperCamelCase_						:					List[Any]      				=			generate_image(CELLS)
    # Uncomment to save the image
    # img.save(f"rule_{rule_num}.png")
    img.show()


