

'''simple docstring'''


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

import numpy
from matplotlib import pyplot

lowerCAmelCase__      				=			0.25 + 0.0j
lowerCAmelCase__      				=			-0.4 + 0.6j
lowerCAmelCase__      				=			-0.1 + 0.651j
lowerCAmelCase__      				=			-2.0
lowerCAmelCase__      				=			56
lowerCAmelCase__      				=			2.0
lowerCAmelCase__      				=			666







def     SCREAMING_SNAKE_CASE(	UpperCamelCase ,UpperCamelCase	)     ->     numpy.ndarray:
	return numpy.exp(UpperCamelCase	) + c_parameter







def     SCREAMING_SNAKE_CASE(	UpperCamelCase ,UpperCamelCase	)     ->     numpy.ndarray:
	return z_values * z_values + c_parameter







def     SCREAMING_SNAKE_CASE(	UpperCamelCase ,UpperCamelCase	)     ->     numpy.ndarray:
	UpperCAmelCase_		:   List[str]													=       numpy.linspace(-window_size ,UpperCamelCase ,UpperCamelCase	)
	UpperCAmelCase_		:   Dict													=       x.reshape((nb_pixels, 1)	)
	UpperCAmelCase_		:   Tuple													=       numpy.linspace(-window_size ,UpperCamelCase ,UpperCamelCase	)
	UpperCAmelCase_		:   Dict													=       y.reshape((1, nb_pixels)	)
	return x + 1.0j * y







def     SCREAMING_SNAKE_CASE(	UpperCamelCase ,UpperCamelCase ,UpperCamelCase ,UpperCamelCase ,UpperCamelCase = None ,)     ->     numpy.ndarray:
	UpperCAmelCase_		:   int													=       z_a.astype('complex64'	)
	for _ in range(UpperCamelCase	):
		UpperCAmelCase_		:   Union[str, Any]													=       eval_function(UpperCamelCase ,UpperCamelCase	)
		if infinity is not None:
			numpy.nan_to_num(UpperCamelCase ,copy=UpperCamelCase ,nan=UpperCamelCase	)
			UpperCAmelCase_		:   List[Any]													=       infinity
	return z_n







def     SCREAMING_SNAKE_CASE(	UpperCamelCase ,UpperCamelCase ,UpperCamelCase ,UpperCamelCase ,)     ->     None:
	UpperCAmelCase_		:   Optional[Any]													=       (abs(UpperCamelCase	)).transpose()
	UpperCAmelCase_		:   List[str]													=       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     SCREAMING_SNAKE_CASE(	)     ->     None:
	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__":
						lowerCAmelCase__      				=			prepare_grid(window_size, nb_pixels)

						ignore_overflow_warnings()  # See file header for explanations

						lowerCAmelCase__      				=			24
						lowerCAmelCase__      				=			2 * abs(c_cauliflower) + 1
						lowerCAmelCase__      				=			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)

						lowerCAmelCase__      				=			64
						lowerCAmelCase__      				=			2 * abs(c_polynomial_a) + 1
						lowerCAmelCase__      				=			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)

						lowerCAmelCase__      				=			161
						lowerCAmelCase__      				=			2 * abs(c_polynomial_a) + 1
						lowerCAmelCase__      				=			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)

						lowerCAmelCase__      				=			12
						lowerCAmelCase__      				=			10000.0
						lowerCAmelCase__      				=			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)









'''simple docstring'''


def     SCREAMING_SNAKE_CASE(	UpperCamelCase	)     ->     int:
	if not isinstance(UpperCamelCase ,UpperCamelCase	):
		raise TypeError('recursive_lucas_number accepts only integer arguments.'	)
	if n_th_number == 0:
		return 2
	if n_th_number == 1:
		return 1

	return recursive_lucas_number(n_th_number - 1	) + recursive_lucas_number(
	    n_th_number - 2	)







def     SCREAMING_SNAKE_CASE(	UpperCamelCase	)     ->     int:
	if not isinstance(UpperCamelCase ,UpperCamelCase	):
		raise TypeError('dynamic_lucas_number accepts only integer arguments.'	)
	UpperCAmelCase_						,     UpperCAmelCase_		:   List[str]													=       2, 1
	for _ in range(UpperCamelCase	):
		UpperCAmelCase_						,     UpperCAmelCase_		:   Dict													=       b, a + b
	return a


if __name__ == "__main__":
						from doctest import testmod

						testmod()
						lowerCAmelCase__      				=			int(input("Enter the number of terms in lucas series:\n").strip())
						print("Using recursive function to calculate lucas series:")
						print(" ".join(str(recursive_lucas_number(i)) for i in range(n)))
						print("\nUsing dynamic function to calculate lucas series:")
						print(" ".join(str(dynamic_lucas_number(i)) for i in range(n)))






