





"""simple docstring"""




import unittest

import numpy as np






def       _SCREAMING_SNAKE_CASE		(	_lowercase						:    np.ndarray    ,       _lowercase						:    np.ndarray    ,       _lowercase						:    np.ndarray    ,       _lowercase						:    np.ndarray | None = None    ,       ) ->np.ndarray:






	'''simple docstring'''






	a      :		Tuple	=				np.shape(_lowercase					)
	a      :		Optional[int]	=				np.shape(_lowercase					)
	a      :		Any	=				np.shape(_lowercase					)

	if shape_a[0] != shape_b[0]:
		a      :		Dict	=				(
		    "Expected the same number of rows for A and B. "
		    F"""Instead found A of size {shape_a} and B of size {shape_b}"""
		)
		raise ValueError(_lowercase					)

	if shape_b[1] != shape_c[1]:
		a      :		int	=				(
		    "Expected the same number of columns for B and C. "
		    F"""Instead found B of size {shape_b} and C of size {shape_c}"""
		)
		raise ValueError(_lowercase					)

	a      :		List[str]	=				pseudo_inv
	if a_inv is None:
		try:
			a      :		Union[str, Any]	=				np.linalg.inv(_lowercase					)
		except np.linalg.LinAlgError:
			raise ValueError(
			    "Input matrix A is not invertible. Cannot compute Schur complement."					)

	return mat_c - mat_b.T @ a_inv @ mat_b


class        __UpperCamelCase				(						unittest.TestCase						):






							def     __a   (   self      )	-> None:
								a      :		List[str]	=				np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]      )
								a      :		List[Any]	=				np.array([[0, 3], [3, 0], [2, 3]]      )
								a      :		int	=				np.array([[2, 1], [6, 3]]      )

								a      :		str	=				schur_complement(lowerCAmelCase__      ,					lowerCAmelCase__      ,					lowerCAmelCase__      )

								a      :		Tuple	=				np.block([[a, b], [b.T, c]]      )

								a      :		Tuple	=				np.linalg.det(lowerCAmelCase__      )
								a      :		int	=				np.linalg.det(lowerCAmelCase__      )
								a      :		List[Any]	=				np.linalg.det(lowerCAmelCase__      )

								self.assertAlmostEqual(lowerCAmelCase__      ,					det_a * det_s      )






							def     __a   (   self      )	-> None:
								a      :		int	=				np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]      )
								a      :		Optional[Any]	=				np.array([[0, 3], [3, 0], [2, 3]]      )
								a      :		Optional[Any]	=				np.array([[2, 1], [6, 3]]      )

								with self.assertRaises(lowerCAmelCase__      ):
									schur_complement(lowerCAmelCase__      ,					lowerCAmelCase__      ,					lowerCAmelCase__      )






							def     __a   (   self      )	-> None:
								a      :		Dict	=				np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]      )
								a      :		Tuple	=				np.array([[0, 3], [3, 0], [2, 3]]      )
								a      :		Tuple	=				np.array([[2, 1, 3], [6, 3, 5]]      )

								with self.assertRaises(lowerCAmelCase__      ):
									schur_complement(lowerCAmelCase__      ,					lowerCAmelCase__      ,					lowerCAmelCase__      )


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		unittest.main()









"""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.

from argparse import ArgumentParser

from accelerate.commands.config import get_config_parser
from accelerate.commands.env import env_command_parser
from accelerate.commands.launch import launch_command_parser
from accelerate.commands.test import test_command_parser
from accelerate.commands.tpu import tpu_command_parser






def       _SCREAMING_SNAKE_CASE		(	) ->Dict:






	'''simple docstring'''






	a      :		Any	=				ArgumentParser("Accelerate CLI tool"    ,       usage="accelerate <command> [<args>]"    ,       allow_abbrev=_lowercase					)
	a      :		List[Any]	=				parser.add_subparsers(help="accelerate command helpers"					)

	# Register commands
	get_config_parser(subparsers=_lowercase					)
	env_command_parser(subparsers=_lowercase					)
	launch_command_parser(subparsers=_lowercase					)
	tpu_command_parser(subparsers=_lowercase					)
	test_command_parser(subparsers=_lowercase					)

	# Let's go
	a      :		List[Any]	=				parser.parse_args()

	if not hasattr(_lowercase    ,       "func"					):
		parser.print_help()
		exit(1					)

	# Run
	args.func(_lowercase					)


if __name__ == "__main__":
		main()


