code: 
  
  
  import warnings
  from collections.abc import Callable
  from typing import Any
  
  import numpy
  from matplotlib import pyplot
  
  _SCREAMING_SNAKE_CASE    :				List[str]       =					0.25 + 0.0J
  _SCREAMING_SNAKE_CASE    :				Union[str, Any]       =					-0.4 + 0.6J
  _SCREAMING_SNAKE_CASE    :				Optional[int]       =					-0.1 + 0.6_51J
  _SCREAMING_SNAKE_CASE    :				Dict       =					-2.0
  _SCREAMING_SNAKE_CASE    :				int       =					56
  _SCREAMING_SNAKE_CASE    :				Optional[Any]       =					2.0
  _SCREAMING_SNAKE_CASE    :				Dict       =					6_66
  def     UpperCAmelCase__		(UpperCamelCase_							,UpperCamelCase_       ):
  
  
  
       """simple docstring"""
  
  
  
  
  
  
       return numpy.exp(UpperCamelCase_       ) + c_parameter
  def     UpperCAmelCase__		(UpperCamelCase_							,UpperCamelCase_       ):
  
  
  
       """simple docstring"""
  
  
  
  
  
  
       return z_values * z_values + c_parameter
  def     UpperCAmelCase__		(UpperCamelCase_							,UpperCamelCase_       ):
  
  
  
       """simple docstring"""
  
  
  
  
  
  
       snake_case					=       numpy.linspace(-window_size							,UpperCamelCase_							,UpperCamelCase_       )
       snake_case					=       x.reshape((nb_pixels, 1)       )
       snake_case					=       numpy.linspace(-window_size							,UpperCamelCase_							,UpperCamelCase_       )
       snake_case					=       y.reshape((1, nb_pixels)       )
       return x + 1.0j * y
  def     UpperCAmelCase__		(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_ = None							,):
  
  
  
       """simple docstring"""
  
  
  
  
  
  
       snake_case					=       z_a.astype('''complex64'''       )
       for _ in range(UpperCamelCase_       ):
            snake_case					=       eval_function(UpperCamelCase_							,UpperCamelCase_       )
            if infinity is not None:
                 numpy.nan_to_num(UpperCamelCase_							,copy=UpperCamelCase_							,nan=UpperCamelCase_       )
                 snake_case					=       infinity
       return z_n
  def     UpperCAmelCase__		(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_							,):
  
  
  
       """simple docstring"""
  
  
  
  
  
  
       snake_case					=       (abs(UpperCamelCase_       )).transpose()
       snake_case					=       abs_z_final[::-1, :]
       pyplot.matshow(abs_z_final < escape_radius       )
       pyplot.title(F'''Julia set of ${function_label}$, $c={function_params}$'''       )
       pyplot.show()
  def     UpperCAmelCase__		():
  
  
  
       """simple docstring"""
  
  
  
  
  
  
       warnings.filterwarnings(
           '''ignore'''							,category=UpperCamelCase_							,message='''overflow encountered in multiply'''       )
       warnings.filterwarnings(
           '''ignore'''							,category=UpperCamelCase_							,message='''invalid value encountered in multiply'''							,)
       warnings.filterwarnings(
           '''ignore'''							,category=UpperCamelCase_							,message='''overflow encountered in absolute'''       )
       warnings.filterwarnings(
           '''ignore'''							,category=UpperCamelCase_							,message='''overflow encountered in exp'''       )
  
  
  if __name__ == "__main__":
   _SCREAMING_SNAKE_CASE    :				str       =					prepare_grid(window_size, nb_pixels)
  
   ignore_overflow_warnings()  # See file header for explanations
  
   _SCREAMING_SNAKE_CASE    :				Any       =					24
   _SCREAMING_SNAKE_CASE    :				Dict       =					2 * abs(c_cauliflower) + 1
   _SCREAMING_SNAKE_CASE    :				Optional[Any]       =					iterate_function(
       eval_quadratic_polynomial,
       c_cauliflower,
       nb_iterations,
       z_a,
       infinity=1.1 * escape_radius,
   )
   show_results("z^2+c", c_cauliflower, escape_radius, z_final)
  
   _SCREAMING_SNAKE_CASE    :				List[str]       =					64
   _SCREAMING_SNAKE_CASE    :				Any       =					2 * abs(c_polynomial_a) + 1
   _SCREAMING_SNAKE_CASE    :				List[str]       =					iterate_function(
       eval_quadratic_polynomial,
       c_polynomial_a,
       nb_iterations,
       z_a,
       infinity=1.1 * escape_radius,
   )
   show_results("z^2+c", c_polynomial_a, escape_radius, z_final)
  
   _SCREAMING_SNAKE_CASE    :				List[Any]       =					1_61
   _SCREAMING_SNAKE_CASE    :				List[Any]       =					2 * abs(c_polynomial_a) + 1
   _SCREAMING_SNAKE_CASE    :				Dict       =					iterate_function(
       eval_quadratic_polynomial,
       c_polynomial_a,
       nb_iterations,
       z_a,
       infinity=1.1 * escape_radius,
   )
   show_results("z^2+c", c_polynomial_a, escape_radius, z_final)
  
   _SCREAMING_SNAKE_CASE    :				Optional[Any]       =					12
   _SCREAMING_SNAKE_CASE    :				Dict       =					10000.0
   _SCREAMING_SNAKE_CASE    :				Tuple       =					iterate_function(
       eval_exponential,
       c_exponential,
       nb_iterations,
       z_a + 2,
       infinity=1.0e1_0,
   )
   show_results("e^z+c", c_exponential, escape_radius, z_final)
  
  
  
  
  
style_context: 
  
  
  import torch
  
  from accelerate import Accelerator, DistributedType
  
  class 						A__      :
  
  
  
  
  
  
  
      """simple docstring"""
  
      def __enter__( self					):
           if self.enabled:
                snake_case					=       self.model.no_sync()
                self.model_sync_obj.__enter__()
  
           return self
      def __exit__( self    ,      __snake_case    ,      __snake_case    ,      __snake_case					):
           if self.enabled:
                # Average all models on exit
                self._sync_and_avg_model_params()
                self.model_sync_obj.__exit__(__snake_case    ,      __snake_case    ,      __snake_case					)
      def __init__( self    ,      __snake_case    ,      __snake_case    ,      __snake_case    ,      __snake_case = True					):
           if accelerator.distributed_type not in [
               DistributedType.NO,
               DistributedType.MULTI_CPU,
               DistributedType.MULTI_GPU,
           ]:
                raise NotImplementedError('''LocalSGD is supported only for CPUs and GPUs (no DeepSpeed or MegatronLM)'''					)
           snake_case					=       enabled and accelerator.distributed_type != DistributedType.NO
           snake_case					=       0
           if self.enabled:
                snake_case					=       accelerator
                snake_case					=       model
                snake_case					=       local_sgd_steps
      def 	a_    ( self					):
           self.num_steps += 1
           if not self.enabled:
                return
  
           if self.num_steps % self.local_sgd_steps == 0:
                self._sync_and_avg_model_params()
  
  
  
  
      def 	a_    ( self					):
           self.accelerator.wait_for_everyone()
           with self.accelerator.autocast():
                for param in self.model.parameters():
                     snake_case					=       self.accelerator.reduce(param.data    ,      reduction='''mean'''					)
  
  
  
  
  