from multiprocessing import Lock, Pipe, Process

# lock used to ensure that two processes do not access a pipe at the same time
_lowerCamelCase					:   List[Any]							=		Lock()





def 	__lowerCamelCase							(UpperCAmelCase__     :							List[Any]      , UpperCAmelCase__     :							List[Any]      , UpperCAmelCase__     :							List[Any]      , UpperCAmelCase__     :							Union[str, Any]      , UpperCAmelCase__     :							List[str]      , UpperCAmelCase__     :							List[str]      , UpperCAmelCase__     :							Dict  ):
					global process_lock

					# we perform n swaps since after n swaps we know we are sorted
					# we *could* stop early if we are sorted already, but it takes as long to
					# find out we are sorted as it does to sort the list with this algorithm
					for i in range(0      , 1_0  ):
										if (i + position) % 2 == 0 and r_send is not None:
															# send your value to your right neighbor
															process_lock.acquire()
															r_send[1].send(UpperCAmelCase__  )
															process_lock.release()

															# receive your right neighbor's value
															process_lock.acquire()
															SCREAMING_SNAKE_CASE    			=       rr_cv[0].recv()
															process_lock.release()

															# take the lower value since you are on the left
															SCREAMING_SNAKE_CASE    			=       min(UpperCAmelCase__      , UpperCAmelCase__  )
										elif (i + position) % 2 != 0 and l_send is not None:
															# send your value to your left neighbor
															process_lock.acquire()
															l_send[1].send(UpperCAmelCase__  )
															process_lock.release()

															# receive your left neighbor's value
															process_lock.acquire()
															SCREAMING_SNAKE_CASE    			=       lr_cv[0].recv()
															process_lock.release()

															# take the higher value since you are on the right
															SCREAMING_SNAKE_CASE    			=       max(UpperCAmelCase__      , UpperCAmelCase__  )
    # after all swaps are performed, send the values back to main
					result_pipe[1].send(UpperCAmelCase__  )





def 	__lowerCamelCase							(UpperCAmelCase__     :							List[Any]  ):
					SCREAMING_SNAKE_CASE    			=       []
					SCREAMING_SNAKE_CASE    			=       []
					# initialize the list of pipes where the values will be retrieved
					for _ in arr:
										result_pipe.append(Pipe()  )
					# creates the processes
					# the first and last process only have one neighbor so they are made outside
					# of the loop
					SCREAMING_SNAKE_CASE    			=       Pipe()
					SCREAMING_SNAKE_CASE    			=       Pipe()
					process_array_.append(
					    Process(
					        target=UpperCAmelCase__      , args=(0, arr[0], None, temp_rs, None, temp_rr, result_pipe[0])      , )  )
					SCREAMING_SNAKE_CASE    			=       temp_rs
					SCREAMING_SNAKE_CASE    			=       temp_rr

					for i in range(1      , len(UpperCAmelCase__  ) - 1  ):
										SCREAMING_SNAKE_CASE    			=       Pipe()
										SCREAMING_SNAKE_CASE    			=       Pipe()
										process_array_.append(
										    Process(
										        target=UpperCAmelCase__      , args=(i, arr[i], temp_ls, temp_rs, temp_lr, temp_rr, result_pipe[i])      , )  )
										SCREAMING_SNAKE_CASE    			=       temp_rs
										SCREAMING_SNAKE_CASE    			=       temp_rr

					process_array_.append(
					    Process(
					        target=UpperCAmelCase__      , args=(
					            len(UpperCAmelCase__  ) - 1,
					            arr[len(UpperCAmelCase__  ) - 1],
					            temp_ls,
					            None,
					            temp_lr,
					            None,
					            result_pipe[len(UpperCAmelCase__  ) - 1],
					        )      , )  )

					# start the processes
					for p in process_array_:
										p.start()

					# wait for the processes to end and write their values to the list
					for p in range(0      , len(UpperCAmelCase__  )  ):
										SCREAMING_SNAKE_CASE    			=       result_pipe[p][0].recv()
										process_array_[p].join()
					return arr





def 	__lowerCamelCase							():
					SCREAMING_SNAKE_CASE    			=       list(range(1_0      , 0      , -1  )  )
					print("Initial List"  )
					print(*UpperCAmelCase__  )
					SCREAMING_SNAKE_CASE    			=       odd_even_transposition(UpperCAmelCase__  )
					print("Sorted List\n"  )
					print(*UpperCAmelCase__  )


if __name__ == "__main__":
							main()





import numpy as np





def 	__lowerCamelCase							(UpperCAmelCase__     :							np.ndarray      , UpperCAmelCase__     :							np.ndarray      , UpperCAmelCase__     :							float = 1e-12      , UpperCAmelCase__     :							int = 1_0_0      , ):
					assert np.shape(UpperCAmelCase__  )[0] == np.shape(UpperCAmelCase__  )[1]
					# Ensure proper dimensionality.
					assert np.shape(UpperCAmelCase__  )[0] == np.shape(UpperCAmelCase__  )[0]
					# Ensure inputs are either both complex or both real
					assert np.iscomplexobj(UpperCAmelCase__  ) == np.iscomplexobj(UpperCAmelCase__  )
					SCREAMING_SNAKE_CASE    			=       np.iscomplexobj(UpperCAmelCase__  )
					if is_complex:
										# Ensure complex input_matrix is Hermitian
										assert np.array_equal(UpperCAmelCase__      , input_matrix.conj().T  )

					# Set convergence to False. Will define convergence when we exceed max_iterations
					# or when we have small changes from one iteration to next.

					SCREAMING_SNAKE_CASE    			=       False
					SCREAMING_SNAKE_CASE    			=       0
					SCREAMING_SNAKE_CASE    			=       0
					SCREAMING_SNAKE_CASE    			=       1e12

					while not convergence:
										# Multiple matrix by the vector.
										SCREAMING_SNAKE_CASE    			=       np.dot(UpperCAmelCase__      , UpperCAmelCase__  )
										# Normalize the resulting output vector.
										SCREAMING_SNAKE_CASE    			=       w / np.linalg.norm(UpperCAmelCase__  )
										# Find rayleigh quotient
										# (faster than usual b/c we know vector is normalized already)
										SCREAMING_SNAKE_CASE    			=       vector.conj().T if is_complex else vector.T
										SCREAMING_SNAKE_CASE    			=       np.dot(UpperCAmelCase__      , np.dot(UpperCAmelCase__      , UpperCAmelCase__  )  )

										# Check convergence.
										SCREAMING_SNAKE_CASE    			=       np.abs(lambda_ - lambda_previous  ) / lambda_
										iterations += 1

										if error <= error_tol or iterations >= max_iterations:
															SCREAMING_SNAKE_CASE    			=       True

										SCREAMING_SNAKE_CASE    			=       lambda_

					if is_complex:
										SCREAMING_SNAKE_CASE    			=       np.real(lambda_  )

					return lambda_, vector





def 	__lowerCamelCase							():
					SCREAMING_SNAKE_CASE    			=       np.array([[4_1, 4, 2_0], [4, 2_6, 3_0], [2_0, 3_0, 5_0]]  )
					SCREAMING_SNAKE_CASE    			=       np.array([4_1, 4, 2_0]  )
					SCREAMING_SNAKE_CASE    			=       real_input_matrix.astype(np.complexaaa  )
					SCREAMING_SNAKE_CASE    			=       np.triu(1j * complex_input_matrix      , 1  )
					complex_input_matrix += imag_matrix
					complex_input_matrix += -1 * imag_matrix.T
					SCREAMING_SNAKE_CASE    			=       np.array([4_1, 4, 2_0]  ).astype(np.complexaaa  )

					for problem_type in ["real", "complex"]:
										if problem_type == "real":
															SCREAMING_SNAKE_CASE    			=       real_input_matrix
															SCREAMING_SNAKE_CASE    			=       real_vector
										elif problem_type == "complex":
															SCREAMING_SNAKE_CASE    			=       complex_input_matrix
															SCREAMING_SNAKE_CASE    			=       complex_vector

										# Our implementation.
										SCREAMING_SNAKE_CASE			,   SCREAMING_SNAKE_CASE    			=       power_iteration(UpperCAmelCase__      , UpperCAmelCase__  )

										# Numpy implementation.

										# Get eigenvalues and eigenvectors using built-in numpy
										# eigh (eigh used for symmetric or hermetian matrices).
										SCREAMING_SNAKE_CASE			,   SCREAMING_SNAKE_CASE    			=       np.linalg.eigh(UpperCAmelCase__  )
										# Last eigenvalue is the maximum one.
										SCREAMING_SNAKE_CASE    			=       eigen_values[-1]
										# Last column in this matrix is eigenvector corresponding to largest eigenvalue.
										SCREAMING_SNAKE_CASE    			=       eigen_vectors[:, -1]

										# Check our implementation and numpy gives close answers.
										assert np.abs(eigen_value - eigen_value_max  ) <= 1e-6
										# Take absolute values element wise of each eigenvector.
										# as they are only unique to a minus sign.
										assert np.linalg.norm(np.abs(UpperCAmelCase__  ) - np.abs(UpperCAmelCase__  )  ) <= 1e-6


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							test_power_iteration()




