
'''simple docstring'''
import hashlib
from typing import Union







def 							A_  (    __SCREAMING_SNAKE_CASE    :	Union[str, int, bytes]			)					->							bytes:





  """simple docstring"""

  if isinstance(__lowerCAmelCase      ,  __lowerCAmelCase			):
    # Data already in bytes, returns as it as
    return hash_data
  elif isinstance(__lowerCAmelCase      ,  __lowerCAmelCase			):
    # We keep the data as it as for it ot be later encoded to UTF-8
    # However replace `\\` with `/` for Windows compatibility
    __A		:  int       				=		hash_data.replace("""\\"""      ,  """/"""			)
  elif isinstance(__lowerCAmelCase      ,  __lowerCAmelCase			):
    __A		:  Union[str, Any]       				=		str(__lowerCAmelCase			)
  else:
    # If data is not of the required type, raise error
    raise InvalidKeyError(__lowerCAmelCase			)

  return hash_data.encode("""utf-8"""			)







class 			__A					(			SCREAMING_SNAKE_CASE__      ):
 def __init__( self      :     List[str]					, lowerCamelCase      :     List[Any]							):



   """simple docstring"""





   __A		:  int       				=		"\nFAILURE TO GENERATE DATASET: Invalid key type detected"
   __A		:  Tuple       				=		f"\nFound Key {hash_data} of type {type(lowerCAmelCase__							)}"
   __A		:  str       				=		"\nKeys should be either str, int or bytes type"
   super().__init__(f"{self.prefix}{self.err_msg}{self.suffix}"							)







class 			__A					(			SCREAMING_SNAKE_CASE__      ):
 def __init__( self      :     Tuple					, lowerCamelCase      :     Optional[Any]					, lowerCamelCase      :     Union[str, Any]					, lowerCamelCase      :     int=""							):



   """simple docstring"""





   __A		:  Optional[int]       				=		key
   __A		:  Tuple       				=		duplicate_key_indices
   __A		:  int       				=		fix_msg
   __A		:  List[Any]       				=		"Found multiple examples generated with the same key"
   if len(lowerCAmelCase__							) <= 20:
     __A		:  Optional[Any]       				=		f"\nThe examples at index {', '.join(lowerCAmelCase__							)} have the key {key}"
   else:
     __A		:  Union[str, Any]       				=		f"\nThe examples at index {', '.join(duplicate_key_indices[:20]							)}... ({len(lowerCAmelCase__							) - 20} more) have the key {key}"
   __A		:  List[Any]       				=		"\n" + fix_msg if fix_msg else ""
   super().__init__(f"{self.prefix}{self.err_msg}{self.suffix}"							)







class 			__A					:
 def __init__( self      :     List[str]					, lowerCamelCase      :     str							):



   """simple docstring"""





   __A		:  Union[str, Any]       				=		hashlib.mda(_as_bytes(lowerCAmelCase__							)							)






 def 		lowercase_( self      :     Tuple					, lowerCamelCase      :     Tuple							):



   """simple docstring"""





   __A		:  Any       				=		self._split_mda.copy()
   __A		:  List[str]       				=		_as_bytes(lowerCAmelCase__							)
   mda.update(lowerCAmelCase__							)
   # Convert to integer with hexadecimal conversion
   return int(mda.hexdigest()					, 16							)









"""simple docstring"""
import numpy as np
from numpy import floataa
from numpy.typing import NDArray






def 				__lowerCAmelCase					(					__lowerCAmelCase			:		NDArray[floataa]  ,	__lowerCAmelCase			:		NDArray[floataa]						)    ->       NDArray[floataa]:
 _UpperCamelCase      ,	_UpperCamelCase      :	Optional[Any]					      =  np.shape(__lowerCAmelCase						)

 _UpperCamelCase      :	NDArray[floataa]					      =  np.zeros((rows, 1)  ,	dtype=__lowerCAmelCase						)
 for row in reversed(range(__lowerCAmelCase						)						):
  _UpperCamelCase      :	List[str]					      =  0
  for col in range(row + 1  ,	__lowerCAmelCase						):
   total += coefficients[row, col] * x[col]

  _UpperCamelCase      :	Dict					      =  (vector[row] - total) / coefficients[row, row]

 return x






def 				__lowerCAmelCase					(					__lowerCAmelCase			:		NDArray[floataa]  ,	__lowerCAmelCase			:		NDArray[floataa]						)    ->       NDArray[floataa]:
 _UpperCamelCase      ,	_UpperCamelCase      :	Optional[Any]					      =  np.shape(__lowerCAmelCase						)
 if rows != columns:
  return np.array(()  ,	dtype=__lowerCAmelCase						)

 # augmented matrix
 _UpperCamelCase      :	NDArray[floataa]					      =  np.concatenate((coefficients, vector)  ,	axis=1						)
 _UpperCamelCase      :	List[str]					      =  augmented_mat.astype("float64"						)

 # scale the matrix leaving it triangular
 for row in range(rows - 1						):
  _UpperCamelCase      :	Optional[Any]					      =  augmented_mat[row, row]
  for col in range(row + 1  ,	__lowerCAmelCase						):
   _UpperCamelCase      :	Union[str, Any]					      =  augmented_mat[col, row] / pivot
   augmented_mat[col, :] -= factor * augmented_mat[row, :]

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

 return x


if __name__ == "__main__":
    import doctest

    doctest.testmod()



