






"""simple docstring"""





import numpy as np






def     A(  snake_case_						,       snake_case_		):
       """simple docstring"""





       lowercase__:    Tuple        =      np.array(snake_case_		)
       lowercase__:    Tuple        =      np.array(snake_case_		)

       lowercase__:    Optional[int]        =      abs(predict - actual		)
       lowercase__:    Optional[int]        =      difference.mean()

       return score






def     A(  snake_case_						,       snake_case_		):
       """simple docstring"""





       lowercase__:    List[str]        =      np.array(snake_case_		)
       lowercase__:    Optional[Any]        =      np.array(snake_case_		)

       lowercase__:    int        =      predict - actual
       lowercase__:    str        =      np.square(snake_case_		)

       lowercase__:    List[str]        =      square_diff.mean()
       return score






def     A(  snake_case_						,       snake_case_		):
       """simple docstring"""





       lowercase__:    Optional[int]        =      np.array(snake_case_		)
       lowercase__:    str        =      np.array(snake_case_		)

       lowercase__:    List[Any]        =      predict - actual
       lowercase__:    Tuple        =      np.square(snake_case_		)
       lowercase__:    Union[str, Any]        =      square_diff.mean()
       lowercase__:    str        =      np.sqrt(snake_case_		)
       return score






def     A(  snake_case_						,       snake_case_		):
       """simple docstring"""





       lowercase__:    Optional[int]        =      np.array(snake_case_		)
       lowercase__:    Optional[int]        =      np.array(snake_case_		)

       lowercase__:    Any        =      np.log(predict + 1		)
       lowercase__:    Optional[Any]        =      np.log(actual + 1		)

       lowercase__:    Optional[Any]        =      log_predict - log_actual
       lowercase__:    str        =      np.square(snake_case_		)
       lowercase__:    Any        =      square_diff.mean()

       lowercase__:    int        =      np.sqrt(snake_case_		)

       return score






def     A(  snake_case_						,       snake_case_		):
       """simple docstring"""





       lowercase__:    Optional[int]        =      np.array(snake_case_		)
       lowercase__:    Tuple        =      np.array(snake_case_		)

       lowercase__:    Union[str, Any]        =      predict - actual
       lowercase__:    Any        =      np.sum(snake_case_		) / len(snake_case_		)
       lowercase__:    int        =      np.sum(snake_case_		) / len(snake_case_		)
       # print(numerator, denumerator)
       lowercase__:    Any        =      float(snake_case_		) / denumerator * 100

       return score







def     A(  snake_case_						,       snake_case_		):
       """simple docstring"""





       return np.mean(np.array(snake_case_		) == np.array(snake_case_		)		)














"""simple docstring"""





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 + 0.651j
UpperCamelCase			=      -2.0
UpperCamelCase			=      56
UpperCamelCase			=      2.0
UpperCamelCase			=      6_66






def     A(  snake_case_						,       snake_case_		):
       """simple docstring"""





       return numpy.exp(snake_case_		) + c_parameter






def     A(  snake_case_						,       snake_case_		):
       """simple docstring"""





       return z_values * z_values + c_parameter






def     A(  snake_case_						,       snake_case_		):
       """simple docstring"""





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






def     A(  snake_case_						,       snake_case_						,       snake_case_						,       snake_case_						,       snake_case_ = None						,       ):
       """simple docstring"""





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






def     A(  snake_case_						,       snake_case_						,       snake_case_						,       snake_case_						,       ):
       """simple docstring"""





       lowercase__:    Union[str, Any]        =      (abs(snake_case_		)).transpose()
       lowercase__:    List[Any]        =      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     A(  ):
       """simple docstring"""





       warnings.filterwarnings(
           "ignore"						,       category=snake_case_						,       message="overflow encountered in multiply"		)
       warnings.filterwarnings(
           "ignore"						,       category=snake_case_						,       message="invalid value encountered in multiply"						,       )
       warnings.filterwarnings(
           "ignore"						,       category=snake_case_						,       message="overflow encountered in absolute"		)
       warnings.filterwarnings(
           "ignore"						,       category=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			=      24
  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			=      64
  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_61
  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			=      12
  UpperCamelCase			=      10_000.0
  UpperCamelCase			=      iterate_function(
      eval_exponential,
      c_exponential,
      nb_iterations,
      z_a + 2,
      infinity=1.0e10,
  )
  show_results("""e^z+c""", c_exponential, escape_radius, z_final)






