
'''simple docstring'''
import warnings
from collections.abc import Callable
from typing import Any

import numpy
from matplotlib import pyplot

A__ :		List[str]					=0.2_5 + 0.0j
A__ :		List[str]					=-0.4 + 0.6j
A__ :		str					=-0.1 + 0.651j
A__ :		Optional[Any]					=-2.0
A__ :		Dict					=56
A__ :		List[str]					=2.0
A__ :		Optional[int]					=666







def 							A_  (    __SCREAMING_SNAKE_CASE    :	complex      ,  __SCREAMING_SNAKE_CASE    :	numpy.ndarray			)					->							numpy.ndarray:





  """simple docstring"""

  return numpy.exp(__a			) + c_parameter







def 							A_  (    __SCREAMING_SNAKE_CASE    :	complex      ,  __SCREAMING_SNAKE_CASE    :	numpy.ndarray			)					->							numpy.ndarray:





  """simple docstring"""

  return z_values * z_values + c_parameter







def 							A_  (    __SCREAMING_SNAKE_CASE    :	float      ,  __SCREAMING_SNAKE_CASE    :	int			)					->							numpy.ndarray:





  """simple docstring"""

  __A		:  List[Any]       				=		numpy.linspace(-window_size      ,  __a      ,  __a			)
  __A		:  Optional[int]       				=		x.reshape((nb_pixels, 1)			)
  __A		:  int       				=		numpy.linspace(-window_size      ,  __a      ,  __a			)
  __A		:  Tuple       				=		y.reshape((1, nb_pixels)			)
  return x + 1.0j * y







def 							A_  (    __SCREAMING_SNAKE_CASE    :	Callable[[Any, numpy.ndarray], numpy.ndarray]      ,  __SCREAMING_SNAKE_CASE    :	Any      ,  __SCREAMING_SNAKE_CASE    :	int      ,  __SCREAMING_SNAKE_CASE    :	numpy.ndarray      ,  __SCREAMING_SNAKE_CASE    :	float | None = None      ,  )					->							numpy.ndarray:





  """simple docstring"""

  __A		:  Optional[Any]       				=		z_a.astype("""complex64"""			)
  for _ in range(__a			):
    __A		:  Any       				=		eval_function(__a      ,  __a			)
    if infinity is not None:
      numpy.nan_to_num(__a      ,  copy=__a      ,  nan=__a			)
      __A		:  Tuple       				=		infinity
  return z_n







def 							A_  (    __SCREAMING_SNAKE_CASE    :	str      ,  __SCREAMING_SNAKE_CASE    :	Any      ,  __SCREAMING_SNAKE_CASE    :	float      ,  __SCREAMING_SNAKE_CASE    :	numpy.ndarray      ,  )					->							None:





  """simple docstring"""

  __A		:  Optional[Any]       				=		(abs(__a			)).transpose()
  __A		:  Optional[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_  (    )					->							None:





  """simple docstring"""

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


if __name__ == "__main__":
     A__ :		List[str]					=prepare_grid(window_size, nb_pixels)

     ignore_overflow_warnings()  # See file header for explanations

     A__ :		Optional[Any]					=24
     A__ :		Dict					=2 * abs(c_cauliflower) + 1
     A__ :		Union[str, 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)

     A__ :		List[Any]					=64
     A__ :		Tuple					=2 * abs(c_polynomial_a) + 1
     A__ :		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)

     A__ :		List[str]					=161
     A__ :		Union[str, Any]					=2 * abs(c_polynomial_a) + 1
     A__ :		Tuple					=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)

     A__ :		Any					=12
     A__ :		str					=10_000.0
     A__ :		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)




import numpy as np
class 	_a  :



	"""simple docstring"""



	def __init__(   self       ,  lowerCAmelCase_=5       ,  lowerCAmelCase_=5       ):
		_lowercase   =depth
		_lowercase   =0
		_lowercase   =None
		_lowercase   =None
		_lowercase   =min_leaf_size
		_lowercase   =None


	def __lowerCAmelCase      (   self       ,  lowerCAmelCase_       ,  lowerCAmelCase_       ):
		if labels.ndim != 1:
			print("Error: Input labels must be one dimensional"       )

		return np.mean((labels - prediction) ** 2       )


	def __lowerCAmelCase      (   self       ,  lowerCAmelCase_       ,  lowerCAmelCase_       ):
		if x.ndim != 1:
			print("Error: Input data set must be one dimensional"       )
			return
		if len(lowerCAmelCase_       ) != len(lowerCAmelCase_       ):
			print("Error: X and y have different lengths"       )
			return
		if y.ndim != 1:
			print("Error: Data set labels must be one dimensional"       )
			return

		if len(lowerCAmelCase_       ) < 2 * self.min_leaf_size:
			_lowercase   =np.mean(lowerCAmelCase_       )
			return

		if self.depth == 1:
			_lowercase   =np.mean(lowerCAmelCase_       )
			return

		_lowercase   =0
		_lowercase   =self.mean_squared_error(lowerCAmelCase_       ,  np.mean(lowerCAmelCase_       )       ) * 2
		for i in range(len(lowerCAmelCase_       )       ):
			if len(x[:i]       ) < self.min_leaf_size:
				continue
			elif len(x[i:]       ) < self.min_leaf_size:
				continue
			else:
				_lowercase   =self.mean_squared_error(x[:i]       ,  np.mean(y[:i]       )       )
				_lowercase   =self.mean_squared_error(x[i:]       ,  np.mean(y[i:]       )       )
				_lowercase   =error_left + error_right
				if error < min_error:
					_lowercase   =i
					_lowercase   =error

		if best_split != 0:
			_lowercase   =x[:best_split]
			_lowercase   =y[:best_split]
			_lowercase   =x[best_split:]
			_lowercase   =y[best_split:]

			_lowercase   =x[best_split]
			_lowercase   =DecisionTree(
			    depth=self.depth - 1       ,  min_leaf_size=self.min_leaf_size       )
			_lowercase   =DecisionTree(
			    depth=self.depth - 1       ,  min_leaf_size=self.min_leaf_size       )
			self.left.train(lowerCAmelCase_       ,  lowerCAmelCase_       )
			self.right.train(lowerCAmelCase_       ,  lowerCAmelCase_       )
		else:
			_lowercase   =np.mean(lowerCAmelCase_       )

		return


	def __lowerCAmelCase      (   self       ,  lowerCAmelCase_       ):
		if self.prediction is not None:
			return self.prediction
		elif self.left or self.right is not None:
			if x >= self.decision_boundary:
				return self.right.predict(lowerCAmelCase_       )
			else:
				return self.left.predict(lowerCAmelCase_       )
		else:
			print("Error: Decision tree not yet trained"       )
			return None

class 	_a  :



	"""simple docstring"""



	@staticmethod
	def __lowerCAmelCase      (   lowerCAmelCase_       ,  lowerCAmelCase_       ):
		_lowercase   =float(0       )
		for label in labels:
			squared_error_sum += (label - prediction) ** 2

		return float(squared_error_sum / labels.size       )

def 	__lowerCamelCase							(				)      ->       Union[str, Any]:
	_lowercase   =np.arange(-1.0      ,							1.0      ,							0.005		)
	_lowercase   =np.sin(__a		)

	_lowercase   =DecisionTree(depth=10      ,							min_leaf_size=10		)
	tree.train(__a      ,							__a		)

	_lowercase   =(np.random.rand(10		) * 2) - 1
	_lowercase   =np.array([tree.predict(__a		) for x in test_cases]		)
	_lowercase   =np.mean((predictions - test_cases) ** 2		)

	print("Test values: " + str(__a		)		)
	print("Predictions: " + str(__a		)		)
	print("Average error: " + str(__a		)		)


if __name__ == "__main__":
						main()
						import doctest

						doctest.testmod(name="mean_squarred_error", verbose=True)




