





import unittest

import numpy as np







def        __lowerCamelCase (							__a       :np.ndarray   ,					__a       :np.ndarray   ,					__a       :np.ndarray   ,					__a       :np.ndarray | None = None   ,					)		->    np.ndarray:






		"""simple docstring"""

		A__  				=       np.shape(__a   )
		A__  				=       np.shape(__a   )
		A__  				=       np.shape(__a   )

		if shape_a[0] != shape_b[0]:
				A__  				=       (
				    """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(__a   )

		if shape_b[1] != shape_c[1]:
				A__  				=       (
				    """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(__a   )

		A__  				=       pseudo_inv
		if a_inv is None:
				try:
						A__  				=       np.linalg.inv(__a   )
				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   A      (unittest.TestCase   ):
			'''simple docstring'''




			def        a_	(      self       :   Union[str, Any]       )     ->     None:







					"""simple docstring"""






					A__  				=       np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]       )
					A__  				=       np.array([[0, 3], [3, 0], [2, 3]]       )
					A__  				=       np.array([[2, 1], [6, 3]]       )

					A__  				=       schur_complement(__lowerCAmelCase							,     __lowerCAmelCase							,     __lowerCAmelCase       )

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

					A__  				=       np.linalg.det(__lowerCAmelCase       )
					A__  				=       np.linalg.det(__lowerCAmelCase       )
					A__  				=       np.linalg.det(__lowerCAmelCase       )

					self.assertAlmostEqual(__lowerCAmelCase							,     det_a * det_s       )






			def        a_	(      self       :   str       )     ->     None:







					"""simple docstring"""






					A__  				=       np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]       )
					A__  				=       np.array([[0, 3], [3, 0], [2, 3]]       )
					A__  				=       np.array([[2, 1], [6, 3]]       )

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







			def        a_	(      self       :   List[str]       )     ->     None:







					"""simple docstring"""






					A__  				=       np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]       )
					A__  				=       np.array([[0, 3], [3, 0], [2, 3]]       )
					A__  				=       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()










# Copyright 2023 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 torch

from accelerate import PartialState
from accelerate.utils.operations import broadcast, gather, gather_object, pad_across_processes, reduce







def        __lowerCamelCase (							__a       :List[str]   )		->    Tuple:






		"""simple docstring"""

		return (torch.arange(state.num_processes   ) + 1.0 + (state.num_processes * state.process_index)).to(state.device   )







def        __lowerCamelCase (							__a       :int   )		->    Optional[int]:






		"""simple docstring"""

		A__  				=       create_tensor(__a   )
		A__  				=       gather(__a   )
		assert gathered_tensor.tolist() == list(range(1   ,					state.num_processes**2 + 1   )   )







def        __lowerCamelCase (							__a       :Any   )		->    Any:






		"""simple docstring"""

		A__  				=       [state.process_index]
		A__  				=       gather_object(__a   )
		assert len(__a   ) == state.num_processes, F'{gathered_obj}, {len(__a   )} != {state.num_processes}'
		assert gathered_obj == list(range(state.num_processes   )   ), F'{gathered_obj} != {list(range(state.num_processes   )   )}'







def        __lowerCamelCase (							__a       :List[str]   )		->    List[str]:






		"""simple docstring"""

		A__  				=       create_tensor(__a   )
		A__  				=       broadcast(__a   )
		assert broadcasted_tensor.shape == torch.Size([state.num_processes]   )
		assert broadcasted_tensor.tolist() == list(range(1   ,					state.num_processes + 1   )   )







def        __lowerCamelCase (							__a       :Any   )		->    Any:






		"""simple docstring"""

		if state.is_main_process:
				A__  				=       torch.arange(state.num_processes + 1   ).to(state.device   )
		else:
				A__  				=       torch.arange(state.num_processes   ).to(state.device   )
		A__  				=       pad_across_processes(__a   )
		assert padded_tensor.shape == torch.Size([state.num_processes + 1]   )
		if not state.is_main_process:
				assert padded_tensor.tolist() == list(range(0   ,					state.num_processes   )   ) + [0]







def        __lowerCamelCase (							__a       :Union[str, Any]   )		->    str:






		"""simple docstring"""

		if state.num_processes != 2:
				return
		A__  				=       create_tensor(__a   )
		A__  				=       reduce(__a   ,					"""sum"""   )
		A__  				=       torch.tensor([4.0, 6]   ).to(state.device   )
		assert torch.allclose(__a   ,					__a   ), F'{reduced_tensor} != {truth_tensor}'







def        __lowerCamelCase (							__a       :List[Any]   )		->    List[str]:






		"""simple docstring"""

		if state.num_processes != 2:
				return
		A__  				=       create_tensor(__a   )
		A__  				=       reduce(__a   ,					"""mean"""   )
		A__  				=       torch.tensor([2.0, 3]   ).to(state.device   )
		assert torch.allclose(__a   ,					__a   ), F'{reduced_tensor} != {truth_tensor}'







def        __lowerCamelCase (							__a       :str   )		->    Optional[int]:






		"""simple docstring"""

		main()







def        __lowerCamelCase (							)		->    str:






		"""simple docstring"""

		A__  				=       PartialState()
		state.print(F'State: {state}'   )
		state.print("""testing gather"""   )
		test_gather(__a   )
		state.print("""testing gather_object"""   )
		test_gather_object(__a   )
		state.print("""testing broadcast"""   )
		test_broadcast(__a   )
		state.print("""testing pad_across_processes"""   )
		test_pad_across_processes(__a   )
		state.print("""testing reduce_sum"""   )
		test_reduce_sum(__a   )
		state.print("""testing reduce_mean"""   )
		test_reduce_mean(__a   )


if __name__ == "__main__":
					main()



