UpperCAmelCase					      =							{
    "meter": "m",
    "kilometer": "km",
    "megametre": "Mm",
    "gigametre": "Gm",
    "terametre": "Tm",
    "petametre": "Pm",
    "exametre": "Em",
    "zettametre": "Zm",
    "yottametre": "Ym",
}
# Exponent of the factor(meter)
UpperCAmelCase					      =							{
    "m": 0,
    "km": 3,
    "Mm": 6,
    "Gm": 9,
    "Tm": 1_2,
    "Pm": 1_5,
    "Em": 1_8,
    "Zm": 2_1,
    "Ym": 2_4,
}






def        SCREAMING_SNAKE_CASE_      (		lowerCAmelCase_:			float			,						lowerCAmelCase_:			str			,						lowerCAmelCase_:			str  ):
      snake_case_  :      str  	=							from_type.lower().strip("s"  )
      snake_case_  :      Optional[int]  	=							to_type.lower().strip("s"  )

      snake_case_  :      Union[str, Any]  	=							UNIT_SYMBOL.get(snake_case__			,						snake_case__  )
      snake_case_  :      Dict  	=							UNIT_SYMBOL.get(snake_case__			,						snake_case__  )

      if from_sanitized not in METRIC_CONVERSION:
            snake_case_  :      List[str]  	=							(
                f"Invalid \'from_type\' value: {from_type!r}.\n"
                f"Conversion abbreviations are: {', '.join(snake_case__  )}"
            )
            raise ValueError(snake_case__  )
      if to_sanitized not in METRIC_CONVERSION:
            snake_case_  :      int  	=							(
                f"Invalid \'to_type\' value: {to_type!r}.\n"
                f"Conversion abbreviations are: {', '.join(snake_case__  )}"
            )
            raise ValueError(snake_case__  )
      snake_case_  :      List[str]  	=							METRIC_CONVERSION[from_sanitized]
      snake_case_  :      Any  	=							METRIC_CONVERSION[to_sanitized]
      snake_case_  :      int  	=							1

      if from_exponent > to_exponent:
            snake_case_  :      Optional[int]  	=							from_exponent - to_exponent
      else:
            snake_case_  :      Dict  	=							-(to_exponent - from_exponent)

      return value * pow(1_0			,						snake_case__  )


if __name__ == "__main__":
     from doctest import testmod

     testmod()











import unittest

import numpy as np






def 	UpperCamelCase	(							snake_case__  : np.ndarray						,snake_case__  : np.ndarray						,snake_case__  : np.ndarray						,snake_case__  : np.ndarray | None = None						,):




     '''simple docstring'''






     __snake_case      :Any 							=    np.shape(snake_case__	)
     __snake_case      :List[str] 							=    np.shape(snake_case__	)
     __snake_case      :List[str] 							=    np.shape(snake_case__	)

     if shape_a[0] != shape_b[0]:
          __snake_case      :int 							=    (
              """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(snake_case__	)

     if shape_b[1] != shape_c[1]:
          __snake_case      :List[str] 							=    (
              """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(snake_case__	)

     __snake_case      :Any 							=    pseudo_inv
     if a_inv is None:
          try:
               __snake_case      :Optional[Any] 							=    np.linalg.inv(snake_case__	)
          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       snake_case__ (				unittest.TestCase):

       '''simple docstring'''



       def        __lowercase    (				self     )			->   None:






            '''simple docstring'''





            __snake_case      :List[str] 							=    np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]     )
            __snake_case      :Union[str, Any] 							=    np.array([[0, 3], [3, 0], [2, 3]]     )
            __snake_case      :List[Any] 							=    np.array([[2, 1], [6, 3]]     )

            __snake_case      :int 							=    schur_complement(a__      ,    a__      ,    a__     )

            __snake_case      :Union[str, Any] 							=    np.block([[a, b], [b.T, c]]     )

            __snake_case      :Dict 							=    np.linalg.det(a__     )
            __snake_case      :Tuple 							=    np.linalg.det(a__     )
            __snake_case      :List[Any] 							=    np.linalg.det(a__     )

            self.assertAlmostEqual(a__      ,    det_a * det_s     )



       def        __lowercase    (				self     )			->   None:






            '''simple docstring'''





            __snake_case      :List[Any] 							=    np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]     )
            __snake_case      :Union[str, Any] 							=    np.array([[0, 3], [3, 0], [2, 3]]     )
            __snake_case      :Optional[int] 							=    np.array([[2, 1], [6, 3]]     )

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



       def        __lowercase    (				self     )			->   None:






            '''simple docstring'''





            __snake_case      :Optional[Any] 							=    np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]     )
            __snake_case      :List[str] 							=    np.array([[0, 3], [3, 0], [2, 3]]     )
            __snake_case      :List[Any] 							=    np.array([[2, 1, 3], [6, 3, 5]]     )

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


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     unittest.main()


