
'''simple docstring'''






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 							_snake_case     (  __a ):
	"""simple docstring"""





	_UpperCamelCase							:  Any								=		'''mock'''




	def __init__(						self				: Dict					,						*UpperCamelCase_				: Any					,						UpperCamelCase_				: Optional[Any]					,						**UpperCamelCase_				: Optional[int]      ):
			super().__init__()
			lowerCAmelCase_   :       List[str]    							=LocalFileSystem(*SCREAMING_SNAKE_CASE__					,						**SCREAMING_SNAKE_CASE__      )
			lowerCAmelCase_   :       List[str]    							=Path(SCREAMING_SNAKE_CASE__      ).resolve().as_posix() + '''/'''




	def 	__A      (						self				: Union[str, Any]					,						UpperCamelCase_				: Tuple					,						*UpperCamelCase_				: Tuple					,						**UpperCamelCase_				: Dict      ):
			lowerCAmelCase_   :       Optional[Any]    							=posixpath.join(self.local_root_dir					,						self._strip_protocol(SCREAMING_SNAKE_CASE__      )      )
			return self._fs.mkdir(SCREAMING_SNAKE_CASE__					,						*SCREAMING_SNAKE_CASE__					,						**SCREAMING_SNAKE_CASE__      )




	def 	__A      (						self				: Union[str, Any]					,						UpperCamelCase_				: List[str]					,						*UpperCamelCase_				: Optional[int]					,						**UpperCamelCase_				: str      ):
			lowerCAmelCase_   :       List[str]    							=posixpath.join(self.local_root_dir					,						self._strip_protocol(SCREAMING_SNAKE_CASE__      )      )
			return self._fs.makedirs(SCREAMING_SNAKE_CASE__					,						*SCREAMING_SNAKE_CASE__					,						**SCREAMING_SNAKE_CASE__      )




	def 	__A      (						self				: List[Any]					,						UpperCamelCase_				: List[str]      ):
			lowerCAmelCase_   :       List[Any]    							=posixpath.join(self.local_root_dir					,						self._strip_protocol(SCREAMING_SNAKE_CASE__      )      )
			return self._fs.rmdir(SCREAMING_SNAKE_CASE__      )




	def 	__A      (						self				: str					,						UpperCamelCase_				: Optional[Any]					,						UpperCamelCase_				: Tuple=True					,						*UpperCamelCase_				: str					,						**UpperCamelCase_				: Any      ):
			lowerCAmelCase_   :       str    							=posixpath.join(self.local_root_dir					,						self._strip_protocol(SCREAMING_SNAKE_CASE__      )      )
			lowerCAmelCase_   :       str    							=self._fs.ls(SCREAMING_SNAKE_CASE__					,						detail=SCREAMING_SNAKE_CASE__					,						*SCREAMING_SNAKE_CASE__					,						**SCREAMING_SNAKE_CASE__      )
			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 	__A      (						self				: Any					,						UpperCamelCase_				: Tuple					,						*UpperCamelCase_				: Dict					,						**UpperCamelCase_				: Dict      ):
			lowerCAmelCase_   :       List[Any]    							=posixpath.join(self.local_root_dir					,						self._strip_protocol(SCREAMING_SNAKE_CASE__      )      )
			lowerCAmelCase_   :       int    							=dict(self._fs.info(SCREAMING_SNAKE_CASE__					,						*SCREAMING_SNAKE_CASE__					,						**SCREAMING_SNAKE_CASE__      )      )
			lowerCAmelCase_   :       int    							=out['''name'''][len(self.local_root_dir      ) :]
			return out




	def 	__A      (						self				: Tuple					,						UpperCamelCase_				: Any					,						UpperCamelCase_				: Optional[Any]					,						*UpperCamelCase_				: int					,						**UpperCamelCase_				: Optional[int]      ):
			lowerCAmelCase_   :       Optional[Any]    							=posixpath.join(self.local_root_dir					,						self._strip_protocol(SCREAMING_SNAKE_CASE__      )      )
			lowerCAmelCase_   :       Union[str, Any]    							=posixpath.join(self.local_root_dir					,						self._strip_protocol(SCREAMING_SNAKE_CASE__      )      )
			return self._fs.cp_file(SCREAMING_SNAKE_CASE__					,						SCREAMING_SNAKE_CASE__					,						*SCREAMING_SNAKE_CASE__					,						**SCREAMING_SNAKE_CASE__      )




	def 	__A      (						self				: List[str]					,						UpperCamelCase_				: str					,						*UpperCamelCase_				: Optional[int]					,						**UpperCamelCase_				: Union[str, Any]      ):
			lowerCAmelCase_   :       Optional[Any]    							=posixpath.join(self.local_root_dir					,						self._strip_protocol(SCREAMING_SNAKE_CASE__      )      )
			return self._fs.rm_file(SCREAMING_SNAKE_CASE__					,						*SCREAMING_SNAKE_CASE__					,						**SCREAMING_SNAKE_CASE__      )




	def 	__A      (						self				: Optional[Any]					,						UpperCamelCase_				: Dict					,						*UpperCamelCase_				: str					,						**UpperCamelCase_				: List[Any]      ):
			lowerCAmelCase_   :       str    							=posixpath.join(self.local_root_dir					,						self._strip_protocol(SCREAMING_SNAKE_CASE__      )      )
			return self._fs.rm(SCREAMING_SNAKE_CASE__					,						*SCREAMING_SNAKE_CASE__					,						**SCREAMING_SNAKE_CASE__      )




	def 	__A      (						self				: Tuple					,						UpperCamelCase_				: List[Any]					,						*UpperCamelCase_				: str					,						**UpperCamelCase_				: str      ):
			lowerCAmelCase_   :       Dict    							=posixpath.join(self.local_root_dir					,						self._strip_protocol(SCREAMING_SNAKE_CASE__      )      )
			return self._fs._open(SCREAMING_SNAKE_CASE__					,						*SCREAMING_SNAKE_CASE__					,						**SCREAMING_SNAKE_CASE__      )




	def 	__A      (						self				: Optional[int]					,						UpperCamelCase_				: Optional[Any]      ):
			lowerCAmelCase_   :       Optional[Any]    							=posixpath.join(self.local_root_dir					,						self._strip_protocol(SCREAMING_SNAKE_CASE__      )      )
			return self._fs.created(SCREAMING_SNAKE_CASE__      )




	def 	__A      (						self				: Any					,						UpperCamelCase_				: Union[str, Any]      ):
			lowerCAmelCase_   :       Optional[int]    							=posixpath.join(self.local_root_dir					,						self._strip_protocol(SCREAMING_SNAKE_CASE__      )      )
			return self._fs.modified(SCREAMING_SNAKE_CASE__      )





	@classmethod
	def 	__A      (						cls				: Any					,						UpperCamelCase_				: List[Any]      ):
			lowerCAmelCase_   :       int    							=stringify_path(SCREAMING_SNAKE_CASE__      )
			if path.startswith('''mock://'''      ):
					lowerCAmelCase_   :       Optional[int]    							=path[7:]
			return path







class 							_snake_case     (  __a ):
	"""simple docstring"""





	_UpperCamelCase							:  Optional[int]								=		'''tmp'''
	_UpperCamelCase							:  int								=		None




	def __init__(						self				: int					,						*UpperCamelCase_				: Dict					,						**UpperCamelCase_				: Union[str, Any]      ):
			assert self.tmp_dir is not None, "TmpDirFileSystem.tmp_dir is not set"
			super().__init__(*SCREAMING_SNAKE_CASE__					,						**SCREAMING_SNAKE_CASE__					,						local_root_dir=self.tmp_dir					,						auto_mkdir=SCREAMING_SNAKE_CASE__      )





	@classmethod
	def 	__A      (						cls				: Optional[Any]					,						UpperCamelCase_				: Optional[int]      ):
			lowerCAmelCase_   :       List[Any]    							=stringify_path(SCREAMING_SNAKE_CASE__      )
			if path.startswith('''tmp://'''      ):
					lowerCAmelCase_   :       List[Any]    							=path[6:]
			return path







@pytest.fixture
def 		SCREAMING_SNAKE_CASE__					(							):
		lowerCAmelCase_   :       Tuple    							=MockFileSystem
		lowerCAmelCase_   :       List[Any]    							=TmpDirFileSystem
		yield
		del _fsspec_registry["mock"]
		del _fsspec_registry["tmp"]







@pytest.fixture
def 		SCREAMING_SNAKE_CASE__					(							_SCREAMING_SNAKE_CASE  ,					_SCREAMING_SNAKE_CASE  ):
		lowerCAmelCase_   :       Optional[Any]    							=tmp_path_factory.mktemp('''mockfs'''  )
		return MockFileSystem(local_root_dir=A__  ,					auto_mkdir=A__  )







@pytest.fixture
def 		SCREAMING_SNAKE_CASE__					(							_SCREAMING_SNAKE_CASE  ,					_SCREAMING_SNAKE_CASE  ):
		lowerCAmelCase_   :       int    							=tmp_path_factory.mktemp('''tmpfs'''  )
		with patch.object(A__  ,					'''tmp_dir'''  ,					A__  ):
				yield TmpDirFileSystem()









"""simple docstring"""




import numpy as np
from numpy import floataa
from numpy.typing import NDArray



def 						UpperCAmelCase__ (					A__						,     A__ )   ->   NDArray[floataa]:




   """simple docstring"""
   lowerCamelCase__       ,							lowerCamelCase__						       =      np.shape(A__ )

   lowerCamelCase__						       =      np.zeros((rows, 1)						,     dtype=A__ )
   for row in reversed(range(A__ ) ):
      lowerCamelCase__						       =      0
      for col in range(row + 1						,     A__ ):
         total += coefficients[row, col] * x[col]

      lowerCamelCase__						       =      (vector[row] - total) / coefficients[row, row]

   return x



def 						UpperCAmelCase__ (					A__						,     A__ )   ->   NDArray[floataa]:




   """simple docstring"""
   lowerCamelCase__       ,							lowerCamelCase__						       =      np.shape(A__ )
   if rows != columns:
      return np.array(()						,     dtype=A__ )

   # augmented matrix
   lowerCamelCase__						       =      np.concatenate((coefficients, vector)						,     axis=1 )
   lowerCamelCase__						       =      augmented_mat.astype("float64" )

   # scale the matrix leaving it triangular
   for row in range(rows - 1 ):
      lowerCamelCase__						       =      augmented_mat[row, row]
      for col in range(row + 1						,     A__ ):
         lowerCamelCase__						       =      augmented_mat[col, row] / pivot
         augmented_mat[col, :] -= factor * augmented_mat[row, :]

   lowerCamelCase__						       =      retroactive_resolution(
       augmented_mat[:, 0:columns]						,     augmented_mat[:, columns : columns + 1] )

   return x


if __name__ == "__main__":
     import doctest

     doctest.testmod()




