





'''simple docstring'''

from collections import namedtuple

__lowerCAmelCase							:     Optional[Any]		     =namedtuple("from_to", "from_ to")

__lowerCAmelCase							:     Union[str, Any]		     ={
    "cubicmeter": from_to(1, 1),
    "litre": from_to(0.001, 1000),
    "kilolitre": from_to(1, 1),
    "gallon": from_to(0.00454, 264.172),
    "cubicyard": from_to(0.76455, 1.30795),
    "cubicfoot": from_to(0.028, 35.3147),
    "cup": from_to(0.000236588, 4226.75),
}





def 						UpperCamelCase    (							_lowerCamelCase : float						,	_lowerCamelCase : str						,	_lowerCamelCase : str	):
    if from_type not in METRIC_CONVERSION:
        raise ValueError(
            F"Invalid 'from_type' value: {from_type!r}  Supported values are:\n"
            + ", ".join(_lowerCamelCase	)	)
    if to_type not in METRIC_CONVERSION:
        raise ValueError(
            F"Invalid 'to_type' value: {to_type!r}.  Supported values are:\n"
            + ", ".join(_lowerCamelCase	)	)
    return value * METRIC_CONVERSION[from_type].from_ * METRIC_CONVERSION[to_type].to


if __name__ == "__main__":
  import doctest

  doctest.testmod()









'''simple docstring'''

import unittest

import numpy as np





def 						UpperCamelCase    (							_lowerCamelCase : np.ndarray						,	_lowerCamelCase : np.ndarray						,	_lowerCamelCase : np.ndarray						,	_lowerCamelCase : np.ndarray | None = None						,	):
    A__    =      np.shape(_lowerCamelCase	)
    A__    =      np.shape(_lowerCamelCase	)
    A__    =      np.shape(_lowerCamelCase	)

    if shape_a[0] != shape_b[0]:
        A__    =      (
            "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(_lowerCamelCase	)

    if shape_b[1] != shape_c[1]:
        A__    =      (
            "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(_lowerCamelCase	)

    A__    =      pseudo_inv
    if a_inv is None:
        try:
            A__    =      np.linalg.inv(_lowerCamelCase	)
        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        UpperCAmelCase     (	unittest.TestCase    ):
 def 					UpperCAmelCase_							(    self				:Any							)->							None:
     A__    =      np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]							)
     A__    =      np.array([[0, 3], [3, 0], [2, 3]]							)
     A__    =      np.array([[2, 1], [6, 3]]							)

     A__    =      schur_complement(lowercase_						,	lowercase_						,	lowercase_							)

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

     A__    =      np.linalg.det(lowercase_							)
     A__    =      np.linalg.det(lowercase_							)
     A__    =      np.linalg.det(lowercase_							)

     self.assertAlmostEqual(lowercase_						,	det_a * det_s							)
 def 					UpperCAmelCase_							(    self				:Dict							)->							None:
     A__    =      np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]							)
     A__    =      np.array([[0, 3], [3, 0], [2, 3]]							)
     A__    =      np.array([[2, 1], [6, 3]]							)

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



 def 					UpperCAmelCase_							(    self				:Union[str, Any]							)->							None:
     A__    =      np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]							)
     A__    =      np.array([[0, 3], [3, 0], [2, 3]]							)
     A__    =      np.array([[2, 1, 3], [6, 3, 5]]							)

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


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  unittest.main()



