





'''simple docstring'''

def    _a    (							lowerCAmelCase_	):





						"""simple docstring"""



						_snake_case		:	int					     =     current_set.copy()
						for row_index, row in enumerate(lowerCAmelCase_	):
												_snake_case		:	List[Any]					     =     row[0]
												for column_index, column in enumerate(lowerCAmelCase_	):
																		if magnitude == 0:
																								_snake_case		:	Dict					     =     column
																								continue
																		_snake_case		:	Tuple					     =     column / magnitude
    # Subtract to cancel term
						_snake_case		:	Any					     =     current_set[0]
						_snake_case		:	Optional[Any]					     =     [first_row]
						_snake_case		:	List[Any]					     =     current_set[1::]
						for row in current_set:
												_snake_case		:	Optional[Any]					     =     []
												# If first term is 0, it is already in form we want, so we preserve it
												if row[0] == 0:
																		final_set.append(lowerCAmelCase_	)
																		continue
												for column_index in range(len(lowerCAmelCase_	)	):
																		temp_row.append(first_row[column_index] - row[column_index]	)
												final_set.append(lowerCAmelCase_	)
						# Create next recursion iteration set
						if len(final_set[0]	) != 3:
												_snake_case		:	int					     =     final_set[0]
												_snake_case		:	List[Any]					     =     []
												_snake_case		:	str					     =     []
												for row in final_set[1::]:
																		current_first_column.append(row[0]	)
																		next_iteration.append(row[1::]	)
												_snake_case		:	int					     =     simplify(lowerCAmelCase_	)
												for i in range(len(lowerCAmelCase_	)	):
																		resultant[i].insert(0			,      current_first_column[i]	)
												resultant.insert(0			,      lowerCAmelCase_	)
												_snake_case		:	Union[str, Any]					     =     resultant
						return final_set




def    _a    (							lowerCAmelCase_	):





						"""simple docstring"""



						if len(lowerCAmelCase_	) == 0:
												raise IndexError('''solve_simultaneous() requires n lists of length n+1'''	)
						_snake_case		:	int					     =     len(lowerCAmelCase_	) + 1
						if any(len(lowerCAmelCase_	) != _length for item in equations	):
												raise IndexError('''solve_simultaneous() requires n lists of length n+1'''	)
						for row in equations:
												if any(not isinstance(lowerCAmelCase_			,      (int, float)	) for column in row	):
																		raise ValueError('''solve_simultaneous() requires lists of integers'''	)
						if len(lowerCAmelCase_	) == 1:
												return [equations[0][-1] / equations[0][0]]
						_snake_case		:	Tuple					     =     equations.copy()
						if any(0 in row for row in data_set	):
												_snake_case		:	List[str]					     =     data_set.copy()
												_snake_case		:	str					     =     []
												for row_index, row in enumerate(lowerCAmelCase_	):
																		if 0 not in row:
																								_snake_case		:	Optional[int]					     =     data_set.pop(lowerCAmelCase_	)
																								break
												if not full_row:
																		raise ValueError('''solve_simultaneous() requires at least 1 full equation'''	)
												data_set.insert(0			,      lowerCAmelCase_	)
						_snake_case		:	List[str]					     =     data_set.copy()
						_snake_case		:	Any					     =     simplify(lowerCAmelCase_	)
						_snake_case		:	str					     =     simplified[::-1]
						_snake_case		:	list					     =     []
						for row in simplified:
												_snake_case		:	List[Any]					     =     row[-1]
												if not solutions:
																		if row[-2] == 0:
																								solutions.append(0	)
																								continue
																		solutions.append(current_solution / row[-2]	)
																		continue
												_snake_case		:	int					     =     row.copy()[: len(lowerCAmelCase_	) - 1 :]
												while temp_row[0] == 0:
																		temp_row.pop(0	)
												if len(lowerCAmelCase_	) == 0:
																		solutions.append(0	)
																		continue
												_snake_case		:	str					     =     temp_row[1::]
												_snake_case		:	Any					     =     temp_row[::-1]
												for column_index, column in enumerate(lowerCAmelCase_	):
																		current_solution -= column * solutions[column_index]
												solutions.append(lowerCAmelCase_	)
						_snake_case		:	Dict					     =     []
						for item in solutions:
												final.append(float(round(lowerCAmelCase_			,      5	)	)	)
						return final[::-1]


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			UpperCAmelCase					:		str		=							[
			    [2, 1, 1, 1, 1, 4],
			    [1, 2, 1, 1, 1, 5],
			    [1, 1, 2, 1, 1, 6],
			    [1, 1, 1, 2, 1, 7],
			    [1, 1, 1, 1, 2, 8],
			]
			print(solve_simultaneous(eq))
			print(solve_simultaneous([[4, 2]]))









'''simple docstring'''

# 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.
from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


UpperCAmelCase					:		Dict		=							{'configuration_timm_backbone': ['TimmBackboneConfig']}


try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCAmelCase					:		Union[str, Any]		=							['TimmBackbone']


if TYPE_CHECKING:
   from .configuration_timm_backbone import TimmBackboneConfig

   try:
      if not is_torch_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_timm_backbone import TimmBackbone

else:
   import sys

   UpperCAmelCase					:		Dict		=							_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)


