code: 
  
  
  
  
  
  
  # 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     __a						:
   # setable values
   _lowerCAmelCase : Optional[jnp.ndarray] 				=				None
   _lowerCAmelCase : Optional[jnp.ndarray] 				=				None
   _lowerCAmelCase : Optional[jnp.ndarray] 				=				None
  
  
  
  
  
  
  
   @classmethod
   def       __lowercase      (	cls      :     Optional[Any]		):
  
  
        '''simple docstring'''
  
  
  
  
  
  
        return cls()
  
  
  
  
  
  
  
  @dataclass
  class     __a						(					A__ ):
   _lowerCAmelCase : ScoreSdeVeSchedulerState
   _lowerCAmelCase : jnp.ndarray
   _lowerCAmelCase : Optional[jnp.ndarray] 				=				None
  
  
  
  
  
  
  
  class     __a						(					A__ ,     A__ ):
  
  
  
  
  
  
  
   @property
   def       __lowercase      (	self      :     Dict		):
  
  
        '''simple docstring'''
  
  
  
  
  
  
        return True
  
  
  
  
  
  
  
   @register_to_config
   def __init__(	self      :     List[Any]							,     SCREAMING_SNAKE_CASE      :     int = 20_00							,     SCREAMING_SNAKE_CASE      :     float = 0.1_5							,     SCREAMING_SNAKE_CASE      :     float = 0.0_1							,     SCREAMING_SNAKE_CASE      :     float = 1_3_4_8.0							,     SCREAMING_SNAKE_CASE      :     float = 1e-5							,     SCREAMING_SNAKE_CASE      :     int = 1							,     ):
  
  
        '''simple docstring'''
  
  
  
  
  
  
        pass
  
  
  
  
  
  
  
   def       __lowercase      (	self      :     Union[str, Any]		):
  
  
        '''simple docstring'''
  
  
  
  
  
  
        UpperCamelCase__    :     Dict        =						ScoreSdeVeSchedulerState.create()
        return self.set_sigmas(
            SCREAMING_SNAKE_CASE							,     self.config.num_train_timesteps							,     self.config.sigma_min							,     self.config.sigma_max							,     self.config.sampling_eps							,     )
  
  
  
  
  
  
  
   def       __lowercase      (	self      :     Optional[Any]							,     SCREAMING_SNAKE_CASE      :     ScoreSdeVeSchedulerState							,     SCREAMING_SNAKE_CASE      :     int							,     SCREAMING_SNAKE_CASE      :     Tuple = ()							,     SCREAMING_SNAKE_CASE      :     float = None		):
  
  
        '''simple docstring'''
  
  
  
  
  
  
        UpperCamelCase__    :     Union[str, Any]        =						sampling_eps if sampling_eps is not None else self.config.sampling_eps
  
        UpperCamelCase__    :     Optional[Any]        =						jnp.linspace(1							,     SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE		)
        return state.replace(timesteps=SCREAMING_SNAKE_CASE		)
  
  
  
  
  
  
  
   def       __lowercase      (	self      :     List[Any]							,     SCREAMING_SNAKE_CASE      :     ScoreSdeVeSchedulerState							,     SCREAMING_SNAKE_CASE      :     int							,     SCREAMING_SNAKE_CASE      :     float = None							,     SCREAMING_SNAKE_CASE      :     float = None							,     SCREAMING_SNAKE_CASE      :     float = None							,     ):
  
  
        '''simple docstring'''
  
  
  
  
  
  
        UpperCamelCase__    :     Any        =						sigma_min if sigma_min is not None else self.config.sigma_min
        UpperCamelCase__    :     Any        =						sigma_max if sigma_max is not None else self.config.sigma_max
        UpperCamelCase__    :     int        =						sampling_eps if sampling_eps is not None else self.config.sampling_eps
        if state.timesteps is None:
             UpperCamelCase__    :     int        =						self.set_timesteps(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE		)
  
        UpperCamelCase__    :     str        =						jnp.exp(jnp.linspace(jnp.log(SCREAMING_SNAKE_CASE		)							,     jnp.log(SCREAMING_SNAKE_CASE		)							,     SCREAMING_SNAKE_CASE		)		)
        UpperCamelCase__    :     Tuple        =						jnp.array([sigma_min * (sigma_max / sigma_min) ** t for t in state.timesteps]		)
  
        return state.replace(discrete_sigmas=SCREAMING_SNAKE_CASE							,     sigmas=SCREAMING_SNAKE_CASE		)
  
  
  
  
  
  
  
   def       __lowercase      (	self      :     Tuple							,     SCREAMING_SNAKE_CASE      :     Optional[int]							,     SCREAMING_SNAKE_CASE      :     Union[str, Any]							,     SCREAMING_SNAKE_CASE      :     Any		):
  
  
        '''simple docstring'''
  
  
  
  
  
  
        return jnp.where(timesteps == 0							,     jnp.zeros_like(SCREAMING_SNAKE_CASE		)							,     state.discrete_sigmas[timesteps - 1]		)
  
  
  
  
  
  
  
   def       __lowercase      (	self      :     str							,     SCREAMING_SNAKE_CASE      :     ScoreSdeVeSchedulerState							,     SCREAMING_SNAKE_CASE      :     jnp.ndarray							,     SCREAMING_SNAKE_CASE      :     int							,     SCREAMING_SNAKE_CASE      :     jnp.ndarray							,     SCREAMING_SNAKE_CASE      :     random.KeyArray							,     SCREAMING_SNAKE_CASE      :     bool = True							,     ):
  
  
        '''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__    :     Optional[int]        =						timestep * jnp.ones(
            sample.shape[0]							,     )
        UpperCamelCase__    :     Tuple        =						(timestep * (len(state.timesteps		) - 1)).long()
  
        UpperCamelCase__    :     List[str]        =						state.discrete_sigmas[timesteps]
        UpperCamelCase__    :     Dict        =						self.get_adjacent_sigma(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE		)
        UpperCamelCase__    :     Optional[int]        =						jnp.zeros_like(SCREAMING_SNAKE_CASE		)
        UpperCamelCase__    :     Optional[Any]        =						(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__    :     Union[str, Any]        =						diffusion.flatten()
        UpperCamelCase__    :     Optional[int]        =						broadcast_to_shape_from_left(SCREAMING_SNAKE_CASE							,     sample.shape		)
        UpperCamelCase__    :     Optional[int]        =						drift - diffusion**2 * model_output
  
        #  equation 6: sample noise for the diffusion term of
        UpperCamelCase__    :     Any        =						random.split(SCREAMING_SNAKE_CASE							,     num=1		)
        UpperCamelCase__    :     str        =						random.normal(key=SCREAMING_SNAKE_CASE							,     shape=sample.shape		)
        UpperCamelCase__    :     Tuple        =						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=SCREAMING_SNAKE_CASE							,     prev_sample_mean=SCREAMING_SNAKE_CASE							,     state=SCREAMING_SNAKE_CASE		)
  
  
  
  
  
  
  
   def       __lowercase      (	self      :     Tuple							,     SCREAMING_SNAKE_CASE      :     ScoreSdeVeSchedulerState							,     SCREAMING_SNAKE_CASE      :     jnp.ndarray							,     SCREAMING_SNAKE_CASE      :     jnp.ndarray							,     SCREAMING_SNAKE_CASE      :     random.KeyArray							,     SCREAMING_SNAKE_CASE      :     bool = True							,     ):
  
  
        '''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__    :     Optional[int]        =						random.split(SCREAMING_SNAKE_CASE							,     num=1		)
        UpperCamelCase__    :     str        =						random.normal(key=SCREAMING_SNAKE_CASE							,     shape=sample.shape		)
  
        # compute step size from the model_output, the noise, and the snr
        UpperCamelCase__    :     List[Any]        =						jnp.linalg.norm(SCREAMING_SNAKE_CASE		)
        UpperCamelCase__    :     Optional[Any]        =						jnp.linalg.norm(SCREAMING_SNAKE_CASE		)
        UpperCamelCase__    :     Any        =						(self.config.snr * noise_norm / grad_norm) ** 2 * 2
        UpperCamelCase__    :     Optional[int]        =						step_size * jnp.ones(sample.shape[0]		)
  
        # compute corrected sample: model_output term and noise term
        UpperCamelCase__    :     Any        =						step_size.flatten()
        UpperCamelCase__    :     str        =						broadcast_to_shape_from_left(SCREAMING_SNAKE_CASE							,     sample.shape		)
        UpperCamelCase__    :     int        =						sample + step_size * model_output
        UpperCamelCase__    :     Tuple        =						prev_sample_mean + ((step_size * 2) ** 0.5) * noise
  
        if not return_dict:
             return (prev_sample, state)
  
        return FlaxSdeVeOutput(prev_sample=SCREAMING_SNAKE_CASE							,     state=SCREAMING_SNAKE_CASE		)
  
  
  
  
  
  
  
   def __len__(	self      :     Dict		):
  
  
        '''simple docstring'''
  
  
  
  
  
  
        return self.config.num_train_timesteps
style_context: 
  
  
  
  
  
  
  def 	SCREAMING_SNAKE_CASE							(      __lowerCAmelCase    )				->			str:
       if len(__lowerCAmelCase    ) == 0 or not all(len(__lowerCAmelCase    ) == 2 for pair in coordinates    ):
            raise ValueError("The program cannot work out a fitting polynomial."    )
  
       if len({tuple(__lowerCAmelCase    ) for pair in coordinates}    ) != len(__lowerCAmelCase    ):
            raise ValueError("The program cannot work out a fitting polynomial."    )
  
       UpperCamelCase__    :     List[str]        =						{x for x, _ in coordinates}
       if len(__lowerCAmelCase    ) == 1:
            return f'x={coordinates[0][0]}'
  
       if len(__lowerCAmelCase    ) != len(__lowerCAmelCase    ):
            raise ValueError("The program cannot work out a fitting polynomial."    )
  
       UpperCamelCase__    :     Any        =						len(__lowerCAmelCase    )
  
       UpperCamelCase__    :     str        =						0
       UpperCamelCase__    :     list[list[float]]        =						[]
       # put the x and x to the power values in a matrix
       while count_of_line < x:
            UpperCamelCase__    :     int        =						0
            UpperCamelCase__    :     List[Any]        =						coordinates[count_of_line][0]
            UpperCamelCase__    :     list[float]        =						[]
            while count_in_line < x:
                 count_line.append(a ** (x - (count_in_line + 1))    )
                 count_in_line += 1
            matrix.append(__lowerCAmelCase    )
            count_of_line += 1
  
       UpperCamelCase__    :     List[Any]        =						0
       # put the y values into a vector
       UpperCamelCase__    :     list[float]        =						[]
       while count_of_line < x:
            vector.append(coordinates[count_of_line][1]    )
            count_of_line += 1
  
       UpperCamelCase__    :     Tuple        =						0
  
       while count < x:
            UpperCamelCase__    :     Dict        =						0
            while zahlen < x:
                 if count == zahlen:
                      zahlen += 1
                 if zahlen == x:
                      break
                 UpperCamelCase__    :     Optional[Any]        =						matrix[zahlen][count] / matrix[count][count]
                 for counting_columns, item in enumerate(matrix[count]    ):
                      # manipulating all the values in the matrix
                      matrix[zahlen][counting_columns] -= item * bruch
                 # manipulating the values in the vector
                 vector[zahlen] -= vector[count] * bruch
                 zahlen += 1
            count += 1
  
       UpperCamelCase__    :     Tuple        =						0
       # make solutions
       UpperCamelCase__    :     list[str]        =						[]
       while count < x:
            solution.append(str(vector[count] / matrix[count][count]    )    )
            count += 1
  
       UpperCamelCase__    :     int        =						0
       UpperCamelCase__    :     List[str]        =						"f(x)="
  
       while count < x:
            UpperCamelCase__    :     list[str]        =						solution[count].split("E"    )
            if len(__lowerCAmelCase    ) > 1:
                 UpperCamelCase__    :     Union[str, Any]        =						f'{remove_e[0]}*10^{remove_e[1]}'
            solved += f'x^{x - (count + 1)}*{solution[count]}'
            if count + 1 != x:
                 solved += "+"
            count += 1
  
       return solved
  
  
  if __name__ == "__main__":
   print(points_to_polynomial([]))
   print(points_to_polynomial([[]]))
   print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
   print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
   print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
   print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
   print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
   print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
   print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
   print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))