'''simple docstring'''

# DISCLAIMER: This file is strongly influenced by https://github.com/yang-song/score_sde_pytorch

from dataclasses import dataclass
from typing import Optional, Tuple, Union

import flax
import jax.numpy as jnp
from jax import random

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import FlaxSchedulerMixin, FlaxSchedulerOutput, broadcast_to_shape_from_left




@flax.struct.dataclass
class    lowerCamelCase__  :
   # setable values
   __UpperCAmelCase           =						None
   __UpperCAmelCase           =						None
   __UpperCAmelCase           =						None



   @classmethod
   def  _UpperCamelCase		(    cls     )				->     List[str]:
        """simple docstring"""





        return cls()




@dataclass
class    lowerCamelCase__  (   __snake_case     ):
   __UpperCAmelCase           =						42
   __UpperCAmelCase           =						42
   __UpperCAmelCase           =						None




class    lowerCamelCase__  (   __snake_case       ,				__snake_case     ):



   @property
   def  _UpperCamelCase		(    self     )				->     List[Any]:
        """simple docstring"""





        return True



   @register_to_config
   def __init__(    self					,      lowerCAmelCase__ = 2_000					,      lowerCAmelCase__ = 0.15					,      lowerCAmelCase__ = 0.01					,      lowerCAmelCase__ = 1348.0					,      lowerCAmelCase__ = 1e-5					,      lowerCAmelCase__ = 1					,      )				->     int:
        """simple docstring"""





        pass



   def  _UpperCamelCase		(    self     )				->     str:
        """simple docstring"""





        _UpperCamelCase  :Dict       =ScoreSdeVeSchedulerState.create()
        return self.set_sigmas(
            lowerCAmelCase__					,      self.config.num_train_timesteps					,      self.config.sigma_min					,      self.config.sigma_max					,      self.config.sampling_eps					,      )



   def  _UpperCamelCase		(    self					,      lowerCAmelCase__					,      lowerCAmelCase__					,      lowerCAmelCase__ = ()					,      lowerCAmelCase__ = None     )				->     ScoreSdeVeSchedulerState:
        """simple docstring"""





        _UpperCamelCase  :Tuple       =sampling_eps if sampling_eps is not None else self.config.sampling_eps

        _UpperCamelCase  :List[Any]       =jnp.linspace(1					,      lowerCAmelCase__					,      lowerCAmelCase__     )
        return state.replace(timesteps=lowerCAmelCase__     )



   def  _UpperCamelCase		(    self					,      lowerCAmelCase__					,      lowerCAmelCase__					,      lowerCAmelCase__ = None					,      lowerCAmelCase__ = None					,      lowerCAmelCase__ = None					,      )				->     ScoreSdeVeSchedulerState:
        """simple docstring"""





        _UpperCamelCase  :Tuple       =sigma_min if sigma_min is not None else self.config.sigma_min
        _UpperCamelCase  :List[Any]       =sigma_max if sigma_max is not None else self.config.sigma_max
        _UpperCamelCase  :List[Any]       =sampling_eps if sampling_eps is not None else self.config.sampling_eps
        if state.timesteps is None:
             _UpperCamelCase  :List[str]       =self.set_timesteps(lowerCAmelCase__					,      lowerCAmelCase__					,      lowerCAmelCase__     )

        _UpperCamelCase  :List[str]       =jnp.exp(jnp.linspace(jnp.log(lowerCAmelCase__     )					,      jnp.log(lowerCAmelCase__     )					,      lowerCAmelCase__     )     )
        _UpperCamelCase  :List[Any]       =jnp.array([sigma_min * (sigma_max / sigma_min) ** t for t in state.timesteps]     )

        return state.replace(discrete_sigmas=lowerCAmelCase__					,      sigmas=lowerCAmelCase__     )



   def  _UpperCamelCase		(    self					,      lowerCAmelCase__					,      lowerCAmelCase__					,      lowerCAmelCase__     )				->     Tuple:
        """simple docstring"""





        return jnp.where(timesteps == 0					,      jnp.zeros_like(lowerCAmelCase__     )					,      state.discrete_sigmas[timesteps - 1]     )



   def  _UpperCamelCase		(    self					,      lowerCAmelCase__					,      lowerCAmelCase__					,      lowerCAmelCase__					,      lowerCAmelCase__					,      lowerCAmelCase__					,      lowerCAmelCase__ = True					,      )				->     Union[FlaxSdeVeOutput, Tuple]:
        """simple docstring"""





        if state.timesteps is None:
             raise ValueError(
                 """`state.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"""     )

        _UpperCamelCase  :int       =timestep * jnp.ones(
            sample.shape[0]					,      )
        _UpperCamelCase  :List[Any]       =(timestep * (len(state.timesteps     ) - 1)).long()

        _UpperCamelCase  :List[str]       =state.discrete_sigmas[timesteps]
        _UpperCamelCase  :List[Any]       =self.get_adjacent_sigma(lowerCAmelCase__					,      lowerCAmelCase__					,      lowerCAmelCase__     )
        _UpperCamelCase  :Optional[Any]       =jnp.zeros_like(lowerCAmelCase__     )
        _UpperCamelCase  :Tuple       =(sigma**2 - adjacent_sigma**2) ** 0.5

        # equation 6 in the paper: the model_output modeled by the network is grad_x log pt(x)
        # also equation 47 shows the analog from SDE models to ancestral sampling methods
        _UpperCamelCase  :Optional[Any]       =diffusion.flatten()
        _UpperCamelCase  :List[str]       =broadcast_to_shape_from_left(lowerCAmelCase__					,      sample.shape     )
        _UpperCamelCase  :Tuple       =drift - diffusion**2 * model_output

        #  equation 6: sample noise for the diffusion term of
        _UpperCamelCase  :str       =random.split(lowerCAmelCase__					,      num=1     )
        _UpperCamelCase  :Optional[Any]       =random.normal(key=lowerCAmelCase__					,      shape=sample.shape     )
        _UpperCamelCase  :List[str]       =sample - drift  # subtract because `dt` is a small negative timestep
        # TODO is the variable diffusion the correct scaling term for the noise?
        _UpperCamelCase  :Optional[Any]       =prev_sample_mean + diffusion * noise  # add impact of diffusion field g

        if not return_dict:
             return (prev_sample, prev_sample_mean, state)

        return FlaxSdeVeOutput(prev_sample=lowerCAmelCase__					,      prev_sample_mean=lowerCAmelCase__					,      state=lowerCAmelCase__     )



   def  _UpperCamelCase		(    self					,      lowerCAmelCase__					,      lowerCAmelCase__					,      lowerCAmelCase__					,      lowerCAmelCase__					,      lowerCAmelCase__ = True					,      )				->     Union[FlaxSdeVeOutput, Tuple]:
        """simple docstring"""





        if state.timesteps is None:
             raise ValueError(
                 """`state.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"""     )

        # For small batch sizes, the paper "suggest replacing norm(z) with sqrt(d), where d is the dim. of z"
        # sample noise for correction
        _UpperCamelCase  :Dict       =random.split(lowerCAmelCase__					,      num=1     )
        _UpperCamelCase  :Union[str, Any]       =random.normal(key=lowerCAmelCase__					,      shape=sample.shape     )

        # compute step size from the model_output, the noise, and the snr
        _UpperCamelCase  :int       =jnp.linalg.norm(lowerCAmelCase__     )
        _UpperCamelCase  :List[str]       =jnp.linalg.norm(lowerCAmelCase__     )
        _UpperCamelCase  :Tuple       =(self.config.snr * noise_norm / grad_norm) ** 2 * 2
        _UpperCamelCase  :int       =step_size * jnp.ones(sample.shape[0]     )

        # compute corrected sample: model_output term and noise term
        _UpperCamelCase  :List[Any]       =step_size.flatten()
        _UpperCamelCase  :Optional[int]       =broadcast_to_shape_from_left(lowerCAmelCase__					,      sample.shape     )
        _UpperCamelCase  :str       =sample + step_size * model_output
        _UpperCamelCase  :List[Any]       =prev_sample_mean + ((step_size * 2) ** 0.5) * noise

        if not return_dict:
             return (prev_sample, state)

        return FlaxSdeVeOutput(prev_sample=lowerCAmelCase__					,      state=lowerCAmelCase__     )




   def __len__(    self     )				->     List[Any]:
        """simple docstring"""





        return self.config.num_train_timesteps



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       lowerCAmelCase			(		lowerCAmelCase_			)->			list[int]:
				return [int(lowerCAmelCase_			) for c in f"""{ruleset:08}"""[:8]]



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



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


if __name__ == "__main__":
						_UpperCAmelCase      :	str  =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      :	Dict  =generate_image(CELLS)
						# Uncomment to save the image
						# img.save(f"rule_{rule_num}.png")
						img.show()