code: import numpy as np
  from numpy import floataa
  from numpy.typing import NDArray
  
  
  
  def 							_lowerCamelCase(				__snake_case						,						__snake_case	)  ->   NDArray[floataa]:
    __snake_case       ,       __snake_case		       =     np.shape(__snake_case	)
  
    __snake_case		       =     np.zeros((rows, 1)						,						dtype=__snake_case	)
    for row in reversed(range(__snake_case	)	):
      __snake_case		       =     0
      for col in range(row + 1						,						__snake_case	):
        total += coefficients[row, col] * x[col]
  
      __snake_case		       =     (vector[row] - total) / coefficients[row, row]
  
    return x
  
  
  
  def 							_lowerCamelCase(				__snake_case						,						__snake_case	)  ->   NDArray[floataa]:
    __snake_case       ,       __snake_case		       =     np.shape(__snake_case	)
    if rows != columns:
      return np.array(()						,						dtype=__snake_case	)
  
    # augmented matrix
    __snake_case		       =     np.concatenate((coefficients, vector)						,						axis=1	)
    __snake_case		       =     augmented_mat.astype("float64"	)
  
    # scale the matrix leaving it triangular
    for row in range(rows - 1	):
      __snake_case		       =     augmented_mat[row, row]
      for col in range(row + 1						,						__snake_case	):
        __snake_case		       =     augmented_mat[col, row] / pivot
        augmented_mat[col, :] -= factor * augmented_mat[row, :]
  
    __snake_case		       =     retroactive_resolution(
        augmented_mat[:, 0:columns]						,						augmented_mat[:, columns : columns + 1]	)
  
    return x
  
  
  if __name__ == "__main__":
    import doctest
  
    doctest.testmod()
  
  
  
  
  
  
style_context: import posixpath
  from pathlib import Path
  from unittest.mock import patch
  
  import pytest
  from fsspec.implementations.local import AbstractFileSystem, LocalFileSystem, stringify_path
  from fsspec.registry import _registry as _fsspec_registry
  
  
  
  
  class 					UpperCamelCase	(     snake_case__      ):
  					__UpperCamelCase						=   """mock"""
  
  
  
  
  					def __init__( self :					List[Any]      ,*_lowerCAmelCase :					Optional[int]      ,_lowerCAmelCase :					Union[str, Any]      ,**_lowerCAmelCase :					Union[str, Any]						):
  
  
  							"""simple docstring"""
  
  
  
  
  							super().__init__()
  							__snake_case		       =     LocalFileSystem(*_lowerCAmelCase      ,**_lowerCAmelCase						)
  							__snake_case		       =     Path(_lowerCAmelCase						).resolve().as_posix() + "/"
  
  
  
  
  					def 							UpperCamelCase_						( self :					List[Any]      ,_lowerCAmelCase :					Optional[Any]      ,*_lowerCAmelCase :					Union[str, Any]      ,**_lowerCAmelCase :					Dict						):
  
  
  							"""simple docstring"""
  
  
  
  
  							__snake_case		       =     posixpath.join(self.local_root_dir      ,self._strip_protocol(_lowerCAmelCase						)						)
  							return self._fs.mkdir(_lowerCAmelCase      ,*_lowerCAmelCase      ,**_lowerCAmelCase						)
  
  
  
  
  					def 							UpperCamelCase_						( self :					int      ,_lowerCAmelCase :					Tuple      ,*_lowerCAmelCase :					Optional[Any]      ,**_lowerCAmelCase :					Optional[Any]						):
  
  
  							"""simple docstring"""
  
  
  
  
  							__snake_case		       =     posixpath.join(self.local_root_dir      ,self._strip_protocol(_lowerCAmelCase						)						)
  							return self._fs.makedirs(_lowerCAmelCase      ,*_lowerCAmelCase      ,**_lowerCAmelCase						)
  
  
  
  
  					def 							UpperCamelCase_						( self :					Tuple      ,_lowerCAmelCase :					Any						):
  
  
  							"""simple docstring"""
  
  
  
  
  							__snake_case		       =     posixpath.join(self.local_root_dir      ,self._strip_protocol(_lowerCAmelCase						)						)
  							return self._fs.rmdir(_lowerCAmelCase						)
  
  
  
  
  					def 							UpperCamelCase_						( self :					List[Any]      ,_lowerCAmelCase :					List[Any]      ,_lowerCAmelCase :					str=True      ,*_lowerCAmelCase :					int      ,**_lowerCAmelCase :					List[str]						):
  
  
  							"""simple docstring"""
  
  
  
  
  							__snake_case		       =     posixpath.join(self.local_root_dir      ,self._strip_protocol(_lowerCAmelCase						)						)
  							__snake_case		       =     self._fs.ls(_lowerCAmelCase      ,detail=_lowerCAmelCase      ,*_lowerCAmelCase      ,**_lowerCAmelCase						)
  							if detail:
  									return [{**info, "name": info["name"][len(self.local_root_dir						) :]} for info in out]
  							else:
  									return [name[len(self.local_root_dir						) :] for name in out]
  
  
  
  
  					def 							UpperCamelCase_						( self :					List[str]      ,_lowerCAmelCase :					Any      ,*_lowerCAmelCase :					Any      ,**_lowerCAmelCase :					str						):
  
  
  							"""simple docstring"""
  
  
  
  
  							__snake_case		       =     posixpath.join(self.local_root_dir      ,self._strip_protocol(_lowerCAmelCase						)						)
  							__snake_case		       =     dict(self._fs.info(_lowerCAmelCase      ,*_lowerCAmelCase      ,**_lowerCAmelCase						)						)
  							__snake_case		       =     out["name"][len(self.local_root_dir						) :]
  							return out
  
  
  
  
  					def 							UpperCamelCase_						( self :					Tuple      ,_lowerCAmelCase :					Optional[int]      ,_lowerCAmelCase :					Optional[Any]      ,*_lowerCAmelCase :					int      ,**_lowerCAmelCase :					Optional[int]						):
  
  
  							"""simple docstring"""
  
  
  
  
  							__snake_case		       =     posixpath.join(self.local_root_dir      ,self._strip_protocol(_lowerCAmelCase						)						)
  							__snake_case		       =     posixpath.join(self.local_root_dir      ,self._strip_protocol(_lowerCAmelCase						)						)
  							return self._fs.cp_file(_lowerCAmelCase      ,_lowerCAmelCase      ,*_lowerCAmelCase      ,**_lowerCAmelCase						)
  
  
  
  
  					def 							UpperCamelCase_						( self :					Union[str, Any]      ,_lowerCAmelCase :					int      ,*_lowerCAmelCase :					List[Any]      ,**_lowerCAmelCase :					int						):
  
  
  							"""simple docstring"""
  
  
  
  
  							__snake_case		       =     posixpath.join(self.local_root_dir      ,self._strip_protocol(_lowerCAmelCase						)						)
  							return self._fs.rm_file(_lowerCAmelCase      ,*_lowerCAmelCase      ,**_lowerCAmelCase						)
  
  
  
  
  					def 							UpperCamelCase_						( self :					Optional[Any]      ,_lowerCAmelCase :					str      ,*_lowerCAmelCase :					Optional[int]      ,**_lowerCAmelCase :					int						):
  
  
  							"""simple docstring"""
  
  
  
  
  							__snake_case		       =     posixpath.join(self.local_root_dir      ,self._strip_protocol(_lowerCAmelCase						)						)
  							return self._fs.rm(_lowerCAmelCase      ,*_lowerCAmelCase      ,**_lowerCAmelCase						)
  
  
  
  
  					def 							UpperCamelCase_						( self :					int      ,_lowerCAmelCase :					Optional[int]      ,*_lowerCAmelCase :					str      ,**_lowerCAmelCase :					Optional[Any]						):
  
  
  							"""simple docstring"""
  
  
  
  
  							__snake_case		       =     posixpath.join(self.local_root_dir      ,self._strip_protocol(_lowerCAmelCase						)						)
  							return self._fs._open(_lowerCAmelCase      ,*_lowerCAmelCase      ,**_lowerCAmelCase						)
  
  
  
  
  					def 							UpperCamelCase_						( self :					Union[str, Any]      ,_lowerCAmelCase :					Tuple						):
  
  
  							"""simple docstring"""
  
  
  
  
  							__snake_case		       =     posixpath.join(self.local_root_dir      ,self._strip_protocol(_lowerCAmelCase						)						)
  							return self._fs.created(_lowerCAmelCase						)
  
  
  
  
  					def 							UpperCamelCase_						( self :					Union[str, Any]      ,_lowerCAmelCase :					int						):
  
  
  							"""simple docstring"""
  
  
  
  
  							__snake_case		       =     posixpath.join(self.local_root_dir      ,self._strip_protocol(_lowerCAmelCase						)						)
  							return self._fs.modified(_lowerCAmelCase						)
  
  
  
  
  
  
  
  					@classmethod
  					def 							UpperCamelCase_						( cls :					Dict      ,_lowerCAmelCase :					Dict						):
  
  
  							"""simple docstring"""
  
  
  
  
  							__snake_case		       =     stringify_path(_lowerCAmelCase						)
  							if path.startswith("mock://"						):
  									__snake_case		       =     path[7:]
  							return path
  
  
  
  
  class 					UpperCamelCase	(     snake_case__      ):
  					__UpperCamelCase						=   """tmp"""
  					__UpperCamelCase						=   None
  
  
  
  
  					def __init__( self :					int      ,*_lowerCAmelCase :					Tuple      ,**_lowerCAmelCase :					Union[str, Any]						):
  
  
  							"""simple docstring"""
  
  
  
  
  							assert self.tmp_dir is not None, "TmpDirFileSystem.tmp_dir is not set"
  							super().__init__(*_lowerCAmelCase      ,**_lowerCAmelCase      ,local_root_dir=self.tmp_dir      ,auto_mkdir=_lowerCAmelCase						)
  
  
  
  
  
  
  
  					@classmethod
  					def 							UpperCamelCase_						( cls :					int      ,_lowerCAmelCase :					str						):
  
  
  							"""simple docstring"""
  
  
  
  
  							__snake_case		       =     stringify_path(_lowerCAmelCase						)
  							if path.startswith("tmp://"						):
  									__snake_case		       =     path[6:]
  							return path
  
  
  
  
  @pytest.fixture
  def 							_lowerCamelCase(				)  ->   str:
  		__snake_case		       =     MockFileSystem
  		__snake_case		       =     TmpDirFileSystem
  		yield
  		del _fsspec_registry["mock"]
  		del _fsspec_registry["tmp"]
  
  
  
  @pytest.fixture
  def 							_lowerCamelCase(				__snake_case						,						__snake_case	)  ->   Dict:
  		__snake_case		       =     tmp_path_factory.mktemp("mockfs"	)
  		return MockFileSystem(local_root_dir=__snake_case						,						auto_mkdir=__snake_case	)
  
  
  
  
  
  @pytest.fixture
  def 							_lowerCamelCase(				__snake_case						,						__snake_case	)  ->   List[Any]:
  		__snake_case		       =     tmp_path_factory.mktemp("tmpfs"	)
  		with patch.object(__snake_case						,						"tmp_dir"						,						__snake_case	):
  				yield TmpDirFileSystem()
  
  
  
  
  
  