
"""simple docstring"""




import numpy as np



def 							_lowerCamelCase			(			__a,				__a,				__a = 1E-12,				__a = 100,				):
		assert np.shape(__a     )[0] == np.shape(__a     )[1]
		# Ensure proper dimensionality.
		assert np.shape(__a     )[0] == np.shape(__a     )[0]
		# Ensure inputs are either both complex or both real
		assert np.iscomplexobj(__a     ) == np.iscomplexobj(__a     )
		SCREAMING_SNAKE_CASE_    			=			np.iscomplexobj(__a     )
		if is_complex:
				# Ensure complex input_matrix is Hermitian
				assert np.array_equal(__a,				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(__a,				__a     )
				# Normalize the resulting output vector.
				SCREAMING_SNAKE_CASE_    			=			w / np.linalg.norm(__a     )
				# 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(__a,				np.dot(__a,				__a     )     )

				# 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([[41, 4, 20], [4, 26, 30], [20, 30, 50]]     )
		SCREAMING_SNAKE_CASE_    			=			np.array([41, 4, 20]     )
		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([41, 4, 20]     ).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(__a,				__a     )

				# 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(__a     )
				# 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(__a     ) - np.abs(__a     )     ) <= 1E-6


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						test_power_iteration()

"""simple docstring"""




# Copyright 2021 The HuggingFace Team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

import argparse
import os

from accelerate.test_utils import execute_subprocess_async



def 							_lowerCamelCase			(			__a=None     ):
		if subparsers is not None:
				SCREAMING_SNAKE_CASE_    			=			subparsers.add_parser('''test'''     )
		else:
				SCREAMING_SNAKE_CASE_    			=			argparse.ArgumentParser('''Accelerate test command'''     )

		parser.add_argument(
		    '''--config_file''',				default=__a,				help=(
		        '''The path to use to store the config file. Will default to a file named default_config.yaml in the cache '''
		        '''location, which is the content of the environment `HF_HOME` suffixed with \'accelerate\', or if you don\'t have '''
		        '''such an environment variable, your cache directory (\'~/.cache\' or the content of `XDG_CACHE_HOME`) suffixed '''
		        '''with \'huggingface\'.'''
		    ),				)

		if subparsers is not None:
				parser.set_defaults(func=__a     )
		return parser



def 							_lowerCamelCase			(			__a     ):
		SCREAMING_SNAKE_CASE_    			=			os.path.sep.join(__file__.split(os.path.sep     )[:-2] + ['''test_utils''', '''scripts''', '''test_script.py''']     )

		if args.config_file is None:
				SCREAMING_SNAKE_CASE_    			=			script_name
		else:
				SCREAMING_SNAKE_CASE_    			=			F'--config_file={args.config_file} {script_name}'

		SCREAMING_SNAKE_CASE_    			=			['''accelerate-launch'''] + test_args.split()
		SCREAMING_SNAKE_CASE_    			=			execute_subprocess_async(__a,				env=os.environ.copy()     )
		if result.returncode == 0:
				print('''Test is a success! You are ready for your distributed training!'''     )



def 							_lowerCamelCase			(			):
		SCREAMING_SNAKE_CASE_    			=			test_command_parser()
		SCREAMING_SNAKE_CASE_    			=			parser.parse_args()
		test_command(__a     )


if __name__ == "__main__":
						main()