
lowerCAmelCase__       = {
    "meter": "m",
    "kilometer": "km",
    "megametre": "Mm",
    "gigametre": "Gm",
    "terametre": "Tm",
    "petametre": "Pm",
    "exametre": "Em",
    "zettametre": "Zm",
    "yottametre": "Ym",
}
# Exponent of the factor(meter)
lowerCAmelCase__       = {
    "m": 0,
    "km": 3,
    "Mm": 6,
    "Gm": 9,
    "Tm": 12,
    "Pm": 15,
    "Em": 18,
    "Zm": 21,
    "Ym": 24,
}
def      _lowerCAmelCase(	__A   ,       __A   ,       __A			):
  UpperCAmelCase					      =  from_type.lower().strip("s"			)
  UpperCAmelCase					      =  to_type.lower().strip("s"			)

  UpperCAmelCase					      =  UNIT_SYMBOL.get(_snake_case   ,       _snake_case			)
  UpperCAmelCase					      =  UNIT_SYMBOL.get(_snake_case   ,       _snake_case			)

  if from_sanitized not in METRIC_CONVERSION:
    UpperCAmelCase					      =  (
        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:
    UpperCAmelCase					      =  (
        F"Invalid 'to_type' value: {to_type!r}.\n"
        F"Conversion abbreviations are: {', '.join(_snake_case			)}"
    )
    raise ValueError(_snake_case			)
  UpperCAmelCase					      =  METRIC_CONVERSION[from_sanitized]
  UpperCAmelCase					      =  METRIC_CONVERSION[to_sanitized]
  UpperCAmelCase					      =  1

  if from_exponent > to_exponent:
    UpperCAmelCase					      =  from_exponent - to_exponent
  else:
    UpperCAmelCase					      =  -(to_exponent - from_exponent)

  return value * pow(10   ,       _snake_case			)


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

      testmod()






import unittest

import numpy as np
def      _lowerCAmelCase(	__A   ,       __A   ,       __A   ,       __A = None   ,       ):
  UpperCAmelCase					      =  np.shape(__A			)
  UpperCAmelCase					      =  np.shape(__A			)
  UpperCAmelCase					      =  np.shape(__A			)

  if shape_a[0] != shape_b[0]:
    UpperCAmelCase					      =  (
        "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(__A			)

  if shape_b[1] != shape_c[1]:
    UpperCAmelCase					      =  (
        "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(__A			)

  UpperCAmelCase					      =  pseudo_inv
  if a_inv is None:
    try:
      UpperCAmelCase					      =  np.linalg.inv(__A			)
    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 						__magic_name__    (       unittest.TestCase    ):


 def _UpperCamelCase	(						self		: List[str]    )    ->      None:
   UpperCAmelCase					      =  np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]    )
   UpperCAmelCase					      =  np.array([[0, 3], [3, 0], [2, 3]]    )
   UpperCAmelCase					      =  np.array([[2, 1], [6, 3]]    )

   UpperCAmelCase					      =  schur_complement(lowerCAmelCase__			,						lowerCAmelCase__			,						lowerCAmelCase__    )

   UpperCAmelCase					      =  np.block([[a, b], [b.T, c]]    )

   UpperCAmelCase					      =  np.linalg.det(lowerCAmelCase__    )
   UpperCAmelCase					      =  np.linalg.det(lowerCAmelCase__    )
   UpperCAmelCase					      =  np.linalg.det(lowerCAmelCase__    )

   self.assertAlmostEqual(lowerCAmelCase__			,						det_a * det_s    )


 def _UpperCamelCase	(						self		: str    )    ->      None:
   UpperCAmelCase					      =  np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]    )
   UpperCAmelCase					      =  np.array([[0, 3], [3, 0], [2, 3]]    )
   UpperCAmelCase					      =  np.array([[2, 1], [6, 3]]    )

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


 def _UpperCamelCase	(						self		: Dict    )    ->      None:
   UpperCAmelCase					      =  np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]    )
   UpperCAmelCase					      =  np.array([[0, 3], [3, 0], [2, 3]]    )
   UpperCAmelCase					      =  np.array([[2, 1, 3], [6, 3, 5]]    )

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


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      unittest.main()



