

import warnings
from collections.abc import Callable
from typing import Any

import numpy
from matplotlib import pyplot

__UpperCAmelCase     					=  0.25 + 0.0j
__UpperCAmelCase     					=  -0.4 + 0.6j
__UpperCAmelCase     					=  -0.1 + 0.6_5_1j
__UpperCAmelCase     					=  -2.0
__UpperCAmelCase     					=  5_6
__UpperCAmelCase     					=  2.0
__UpperCAmelCase     					=  6_6_6







def 						_snake_case		(     SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE					)							->   numpy.ndarray:

     """simple docstring"""







     return numpy.exp(SCREAMING_SNAKE_CASE					) + c_parameter







def 						_snake_case		(     SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE					)							->   numpy.ndarray:

     """simple docstring"""







     return z_values * z_values + c_parameter







def 						_snake_case		(     SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE					)							->   numpy.ndarray:

     """simple docstring"""







     _lowerCAmelCase :       Any	   =     numpy.linspace(-window_size		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE					)
     _lowerCAmelCase :       Dict	   =     x.reshape((nb_pixels, 1)					)
     _lowerCAmelCase :       List[str]	   =     numpy.linspace(-window_size		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE					)
     _lowerCAmelCase :       List[str]	   =     y.reshape((1, nb_pixels)					)
     return x + 1.0J * y







def 						_snake_case		(     SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE = None		,				)							->   numpy.ndarray:

     """simple docstring"""







     _lowerCAmelCase :       List[Any]	   =     z_a.astype("complex64"					)
     for _ in range(SCREAMING_SNAKE_CASE					):
          _lowerCAmelCase :       Union[str, Any]	   =     eval_function(SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE					)
          if infinity is not None:
               numpy.nan_to_num(SCREAMING_SNAKE_CASE		,				copy=SCREAMING_SNAKE_CASE		,				nan=SCREAMING_SNAKE_CASE					)
               _lowerCAmelCase :       int	   =     infinity
     return z_n







def 						_snake_case		(     SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE		,				)							->   None:

     """simple docstring"""







     _lowerCAmelCase :       Union[str, Any]	   =     (abs(SCREAMING_SNAKE_CASE					)).transpose()
     _lowerCAmelCase :       Dict	   =     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 						_snake_case		(     )							->   None:

     """simple docstring"""







     warnings.filterwarnings(
         "ignore"		,				category=SCREAMING_SNAKE_CASE		,				message="overflow encountered in multiply"					)
     warnings.filterwarnings(
         "ignore"		,				category=SCREAMING_SNAKE_CASE		,				message="invalid value encountered in multiply"		,				)
     warnings.filterwarnings(
         "ignore"		,				category=SCREAMING_SNAKE_CASE		,				message="overflow encountered in absolute"					)
     warnings.filterwarnings(
         "ignore"		,				category=SCREAMING_SNAKE_CASE		,				message="overflow encountered in exp"					)


if __name__ == "__main__":
  __UpperCAmelCase     					=  prepare_grid(window_size, nb_pixels)

  ignore_overflow_warnings()  # See file header for explanations

  __UpperCAmelCase     					=  2_4
  __UpperCAmelCase     					=  2 * abs(c_cauliflower) + 1
  __UpperCAmelCase     					=  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)

  __UpperCAmelCase     					=  6_4
  __UpperCAmelCase     					=  2 * abs(c_polynomial_a) + 1
  __UpperCAmelCase     					=  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)

  __UpperCAmelCase     					=  1_6_1
  __UpperCAmelCase     					=  2 * abs(c_polynomial_a) + 1
  __UpperCAmelCase     					=  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)

  __UpperCAmelCase     					=  1_2
  __UpperCAmelCase     					=  10000.0
  __UpperCAmelCase     					=  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)










from .hash_table import HashTable
from .number_theory.prime_numbers import is_prime, next_prime





class     __a     (       __UpperCamelCase ):
 def __init__(  self							,					*lowerCAmelCase__							,					**lowerCAmelCase__					)   ->							Any:




        '''simple docstring'''
        super().__init__(*lowerCAmelCase__							,					**lowerCAmelCase__					)
 def 						SCREAMING_SNAKE_CASE__  (  self							,					lowerCAmelCase__							,					lowerCAmelCase__					)   ->							Union[str, Any]:




        '''simple docstring'''
        lowercase__:  str         =  (
            next_prime(value % self.size_table					)
            if not is_prime(value % self.size_table					)
            else value % self.size_table
        )  # gt = bigger than
        return next_prime_gt - (data % next_prime_gt)
 def 						SCREAMING_SNAKE_CASE__  (  self							,					lowerCAmelCase__							,					lowerCAmelCase__							,					lowerCAmelCase__					)   ->							Union[str, Any]:




        '''simple docstring'''
        return (increment * self.__hash_function_a(lowerCAmelCase__							,					lowerCAmelCase__					)) % self.size_table
 def 						SCREAMING_SNAKE_CASE__  (  self							,					lowerCAmelCase__							,					lowerCAmelCase__=None					)   ->							str:




        '''simple docstring'''
        lowercase__:  Dict         =  1
        lowercase__:  str         =  self.hash_function(lowerCAmelCase__					)

        while self.values[new_key] is not None and self.values[new_key] != key:
               lowercase__:  List[Any]         =  (
                   self.__hash_double_function(lowerCAmelCase__							,					lowerCAmelCase__							,					lowerCAmelCase__					)
                   if self.balanced_factor() >= self.lim_charge
                   else None
               )
               if new_key is None:
                      break
               else:
                      i += 1

        return new_key


