



'''simple docstring'''



import numpy as np






class        UpperCAmelCase__						:



					def __init__(     self      ,					UpperCamelCase=5      ,					UpperCamelCase=5  )  ->      List[str]:
						__lowerCAmelCase       				=	depth
						__lowerCAmelCase       				=	0
						__lowerCAmelCase       				=	None
						__lowerCAmelCase       				=	None
						__lowerCAmelCase       				=	min_leaf_size
						__lowerCAmelCase       				=	None



					def 							UpperCAmelCase_			(     self      ,					UpperCamelCase      ,					UpperCamelCase  )  ->      Union[str, Any]:
						if labels.ndim != 1:
							print("Error: Input labels must be one dimensional"  )

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



					def 							UpperCAmelCase_			(     self      ,					UpperCamelCase      ,					UpperCamelCase  )  ->      Optional[int]:
						if x.ndim != 1:
							print("Error: Input data set must be one dimensional"  )
							return
						if len(UpperCamelCase  ) != len(UpperCamelCase  ):
							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(UpperCamelCase  ) < 2 * self.min_leaf_size:
							__lowerCAmelCase       				=	np.mean(UpperCamelCase  )
							return

						if self.depth == 1:
							__lowerCAmelCase       				=	np.mean(UpperCamelCase  )
							return

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

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

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

						return



					def 							UpperCAmelCase_			(     self      ,					UpperCamelCase  )  ->      Optional[Any]:
						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(UpperCamelCase  )
							else:
								return self.left.predict(UpperCamelCase  )
						else:
							print("Error: Decision tree not yet trained"  )
							return None






class        UpperCAmelCase__						:



					@staticmethod
					def 							UpperCAmelCase_			(     UpperCamelCase      ,					UpperCamelCase  )  ->      Optional[Any]:
						__lowerCAmelCase       				=	float(0  )
						for label in labels:
							squared_error_sum += (label - prediction) ** 2

						return float(squared_error_sum / labels.size  )



def 	__lowerCAmelCase       (				):






	'''simple docstring'''




	__lowerCAmelCase       				=	np.arange(-1.0					,		1.0					,		0.0_0_5       )
	__lowerCAmelCase       				=	np.sin(lowerCamelCase       )

	__lowerCAmelCase       				=	DecisionTree(depth=10					,		min_leaf_size=10       )
	tree.train(lowerCamelCase					,		lowerCamelCase       )

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

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


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

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




'''simple docstring'''



def 	__lowerCAmelCase       (				lowerCamelCase :    list[list[int]]					,		lowerCamelCase :    list[list[int]]       ):






	'''simple docstring'''




	__lowerCAmelCase       				=	[]
	__lowerCAmelCase       				=	len(lowerCamelCase       )
	for i in range(lowerCamelCase       ):
		__lowerCAmelCase       				=	[]
		for j in range(lowerCamelCase       ):
			__lowerCAmelCase       				=	0
			for k in range(lowerCamelCase       ):
				__lowerCAmelCase       				=	val + matrix_a[i][k] * matrix_b[k][j]
			list_a.append(lowerCamelCase       )
		matrix_c.append(lowerCamelCase       )
	return matrix_c



def 	__lowerCAmelCase       (				lowerCamelCase :    int       ):






	'''simple docstring'''




	return [[int(row == column       ) for column in range(lowerCamelCase       )] for row in range(lowerCamelCase       )]



def 	__lowerCAmelCase       (				lowerCamelCase :    int       ):






	'''simple docstring'''




	if n <= 1:
		return n
	__lowerCAmelCase       				=	identity(2       )
	__lowerCAmelCase       				=	[[1, 1], [1, 0]]
	__lowerCAmelCase       				=	n - 1
	while n > 0:
		if n % 2 == 1:
			__lowerCAmelCase       				=	multiply(lowerCamelCase					,		lowerCamelCase       )
		__lowerCAmelCase       				=	multiply(lowerCamelCase					,		lowerCamelCase       )
		__lowerCAmelCase       				=	int(n / 2       )
	return res_matrix[0][0]



def 	__lowerCAmelCase       (				lowerCamelCase :    int       ):






	'''simple docstring'''




	if n <= 1:
		return n
	__lowerCAmelCase       				=	0
	__lowerCAmelCase       				=	1
	for _ in range(2					,		n + 1       ):
		__lowerCAmelCase				,							__lowerCAmelCase       				=	fiba, fiba + fiba
	return fiba



def 	__lowerCAmelCase       (				):






	'''simple docstring'''




	for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
		__lowerCAmelCase       				=	int("".join(c for c in ordinal if c in "0123456789"       )       )  # 1000th --> 1000
		print(
		    f'''{ordinal} fibonacci number using matrix exponentiation is '''
		    f'''{nth_fibonacci_matrix(lowerCamelCase       )} and using bruteforce is '''
		    f'''{nth_fibonacci_bruteforce(lowerCamelCase       )}\n'''       )
	# from timeit import timeit
	# print(timeit("nth_fibonacci_matrix(1000000)",
	#              "from main import nth_fibonacci_matrix", number=5))
	# print(timeit("nth_fibonacci_bruteforce(1000000)",
	#              "from main import nth_fibonacci_bruteforce", number=5))
	# 2.3342058970001744
	# 57.256506615000035


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	main()