



"""simple docstring"""
import math
class 				lowerCamelCase  :






					'''simple docstring'''





					def    lowerCAmelCase_				(       self:							Tuple						,     snake_case:							list[list[float]]						,     snake_case:							list[int]						)   ->	int:
											snake_case_ :Any						=			0.0
											snake_case_ :Tuple						=			0.0
											for i in range(len(snake_case						)						):
																	da += math.pow((sample[i] - weights[0][i])						,     2						)
																	da += math.pow((sample[i] - weights[1][i])						,     2						)
																	return 0 if da > da else 1
											return 0






					def    lowerCAmelCase_				(       self:							Optional[int]						,     snake_case:							list[list[int | float]]						,     snake_case:							list[int]						,     snake_case:							int						,     snake_case:							float						)   ->	list[list[int | float]]:
											for i in range(len(snake_case						)						):
																	weights[j][i] += alpha * (sample[i] - weights[j][i])
											return weights

def    A_  (			):







						'''simple docstring'''


						snake_case_ :Dict						=			[[1, 1, 0, 0], [0, 0, 0, 1], [1, 0, 0, 0], [0, 0, 1, 1]]

						# weight initialization ( n, C )
						snake_case_ :List[Any]						=			[[0.2, 0.6, 0.5, 0.9], [0.8, 0.4, 0.7, 0.3]]

						# training
						snake_case_ :Optional[Any]						=			SelfOrganizingMap()
						snake_case_ :Dict						=			3
						snake_case_ :Dict						=			0.5

						for _ in range(_lowercase	):
												for j in range(len(_lowercase	)	):
																		# training sample
																		snake_case_ :List[Any]						=			training_samples[j]

																		# Compute the winning vector
																		snake_case_ :Optional[int]						=			self_organizing_map.get_winner(_lowercase,					_lowercase	)

																		# Update the winning vector
																		snake_case_ :List[str]						=			self_organizing_map.update(_lowercase,					_lowercase,					_lowercase,					_lowercase	)

    # classify test sample
						snake_case_ :str						=			[0, 0, 0, 1]
						snake_case_ :List[Any]						=			self_organizing_map.get_winner(_lowercase,					_lowercase	)

						# results
						print(f"""Clusters that the test sample belongs to : {winner}"""	)
						print(f"""Weights that have been trained : {weights}"""	)


# running the main() function
if __name__ == "__main__":
						main()





"""simple docstring"""
from math import factorial
class 				lowerCamelCase  :






					'''simple docstring'''





					def __init__(       self:							Optional[int]						,     snake_case:							Dict						,     snake_case:							int						)   ->	Tuple:
											snake_case_ :List[Any]						=			real
											if isinstance(snake_case						,     snake_case						):
																	snake_case_ :Tuple						=			[1] * rank
											else:
																	snake_case_ :Optional[Any]						=			rank






					def __repr__(       self:							List[str]						)   ->	Tuple:
											return (
											    f"""{self.real}+"""
											    f"""{'+'.join(str(snake_case						)+'E'+str(n+1						)for n,dual in enumerate(self.duals						)						)}"""
											)






					def    lowerCAmelCase_				(       self:							Optional[int]						)   ->	Optional[int]:
											snake_case_ :Any						=			self.duals.copy()
											while cur[-1] == 0:
																	cur.pop(-1						)
											return Dual(self.real						,     snake_case						)






					def __add__(       self:							Optional[int]						,     snake_case:							Dict						)   ->	List[str]:
											if not isinstance(snake_case						,     snake_case						):
																	return Dual(self.real + other						,     self.duals						)
											snake_case_ :List[Any]						=			self.duals.copy()
											snake_case_ :Tuple						=			other.duals.copy()
											if len(snake_case						) > len(snake_case						):
																	o_dual.extend([1] * (len(snake_case						) - len(snake_case						))						)
											elif len(snake_case						) < len(snake_case						):
																	s_dual.extend([1] * (len(snake_case						) - len(snake_case						))						)
											snake_case_ :Dict						=			[]
											for i in range(len(snake_case						)						):
																	new_duals.append(s_dual[i] + o_dual[i]						)
											return Dual(self.real + other.real						,     snake_case						)

					_A		:			str						=     __add__






					def __sub__(       self:							Tuple						,     snake_case:							Union[str, Any]						)   ->	Tuple:
											return self + other * -1






					def __mul__(       self:							str						,     snake_case:							Tuple						)   ->	Optional[Any]:
											if not isinstance(snake_case						,     snake_case						):
																	snake_case_ :Dict						=			[]
																	for i in self.duals:
																							new_duals.append(i * other						)
																	return Dual(self.real * other						,     snake_case						)
											snake_case_ :int						=			[0] * (len(self.duals						) + len(other.duals						) + 1)
											for i, item in enumerate(self.duals						):
																	for j, jtem in enumerate(other.duals						):
																							new_duals[i + j + 1] += item * jtem
											for k in range(len(self.duals						)						):
																	new_duals[k] += self.duals[k] * other.real
											for index in range(len(other.duals						)						):
																	new_duals[index] += other.duals[index] * self.real
											return Dual(self.real * other.real						,     snake_case						)

					_A		:			int						=     __mul__






					def __truediv__(       self:							List[str]						,     snake_case:							List[str]						)   ->	List[str]:
											if not isinstance(snake_case						,     snake_case						):
																	snake_case_ :Optional[Any]						=			[]
																	for i in self.duals:
																							new_duals.append(i / other						)
																	return Dual(self.real / other						,     snake_case						)
											raise ValueError






					def __floordiv__(       self:							int						,     snake_case:							List[Any]						)   ->	Any:
											if not isinstance(snake_case						,     snake_case						):
																	snake_case_ :Optional[int]						=			[]
																	for i in self.duals:
																							new_duals.append(i // other						)
																	return Dual(self.real // other						,     snake_case						)
											raise ValueError






					def __pow__(       self:							Optional[Any]						,     snake_case:							Optional[int]						)   ->	List[Any]:
											if n < 0 or isinstance(snake_case						,     snake_case						):
																	raise ValueError("""power must be a positive integer"""						)
											if n == 0:
																	return 1
											if n == 1:
																	return self
											snake_case_ :str						=			self
											for _ in range(n - 1						):
																	x *= self
											return x

def    A_  (			_lowercase,					_lowercase,					_lowercase	):







						'''simple docstring'''


						if not callable(_lowercase	):
												raise ValueError("""differentiate() requires a function as input for func"""	)
						if not isinstance(_lowercase,					(float, int)	):
												raise ValueError("""differentiate() requires a float as input for position"""	)
						if not isinstance(_lowercase,					_lowercase	):
												raise ValueError("""differentiate() requires an int as input for order"""	)
						snake_case_ :Optional[Any]						=			Dual(_lowercase,					1	)
						snake_case_ :List[Any]						=			func(_lowercase	)
						if order == 0:
												return result.real
						return result.duals[order - 1] * factorial(_lowercase	)


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						def    A_  (			_lowercase	):







												'''simple docstring'''


												return y**2 * y**4

						print(differentiate(f, 9, 2))
