
'''simple docstring'''





from typing import Any

import numpy as np



def  UpperCamelCase					(							lowerCAmelCase__	):
					'''simple docstring'''
					return np.array_equal(lowerCAmelCase__				,    matrix.conjugate().T	)



def  UpperCamelCase					(							lowerCAmelCase__				,    lowerCAmelCase__	):
					'''simple docstring'''
					lowercase					=		v.conjugate().T
					lowercase					=		v_star.dot(lowerCAmelCase__	)
					assert isinstance(lowerCAmelCase__				,    np.ndarray	)
					return (v_star_dot.dot(lowerCAmelCase__	)) / (v_star.dot(lowerCAmelCase__	))



def  UpperCamelCase					(							):
					'''simple docstring'''
					lowercase					=		np.array([[2, 2 + 1j, 4], [2 - 1j, 3, 1j], [4, -1j, 1]]	)
					lowercase					=		np.array([[1], [2], [3]]	)
					assert is_hermitian(lowerCAmelCase__	), f'{a} is not hermitian.'
					print(rayleigh_quotient(lowerCAmelCase__				,    lowerCAmelCase__	)	)

					lowercase					=		np.array([[1, 2, 4], [2, 3, -1], [4, -1, 1]]	)
					assert is_hermitian(lowerCAmelCase__	), f'{a} is not hermitian.'
					assert rayleigh_quotient(lowerCAmelCase__				,    lowerCAmelCase__	) == float(3	)


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							tests()






class        lowercase	:




							def __init__(       self     ,A__):
												lowercase					=		val
												lowercase					=		None
												lowercase					=		None





							def 				A__   (       self     ,A__):
												if self.val:
																	if val < self.val:
																						if self.left is None:
																											lowercase					=		Node(A__)
																						else:
																											self.left.insert(A__)
																	elif val > self.val:
																						if self.right is None:
																											lowercase					=		Node(A__)
																						else:
																											self.right.insert(A__)
												else:
																	lowercase					=		val



def  UpperCamelCase					(							lowerCAmelCase__				,    lowerCAmelCase__	):
					'''simple docstring'''
					# Recursive traversal
					if root:
										inorder(root.left				,    lowerCAmelCase__	)
										res.append(root.val	)
										inorder(root.right				,    lowerCAmelCase__	)



def  UpperCamelCase					(							lowerCAmelCase__	):
					'''simple docstring'''
					# Build BST
					if len(lowerCAmelCase__	) == 0:
										return arr
					lowercase					=		Node(arr[0]	)
					for i in range(1				,    len(lowerCAmelCase__	)	):
										root.insert(arr[i]	)
					# Traverse BST in order.
					lowercase					=		[]
					inorder(lowerCAmelCase__				,    lowerCAmelCase__	)
					return res


if __name__ == "__main__":
							print(tree_sort([10, 1, 3, 2, 9, 14, 13]))




