





from __future__ import annotations

from math import pi

# Define the Reduced Planck Constant ℏ (H bar), speed of light C, value of
# Pi and the function
A   : Union[str, Any]			=				1.054571817e-34  # unit of ℏ : J * s

A   : Optional[Any]			=				3e8  # unit of c : m * s^-1







def        __lowerCamelCase (							__a       :float   ,					__a       :float   ,					__a       :float   )		->    dict[str, float]:






		"""simple docstring"""

		if (force, area, distance).count(0   ) != 1:
				raise ValueError("""One and only one argument must be 0"""   )
		if force < 0:
				raise ValueError("""Magnitude of force can not be negative"""   )
		if distance < 0:
				raise ValueError("""Distance can not be negative"""   )
		if area < 0:
				raise ValueError("""Area can not be negative"""   )
		if force == 0:
				A__  				=       (REDUCED_PLANCK_CONSTANT * SPEED_OF_LIGHT * pi**2 * area) / (
				    2_4_0 * (distance) ** 4
				)
				return {"force": force}
		elif area == 0:
				A__  				=       (2_4_0 * force * (distance) ** 4) / (
				    REDUCED_PLANCK_CONSTANT * SPEED_OF_LIGHT * pi**2
				)
				return {"area": area}
		elif distance == 0:
				A__  				=       (
				    (REDUCED_PLANCK_CONSTANT * SPEED_OF_LIGHT * pi**2 * area) / (2_4_0 * force)
				) ** (1 / 4)
				return {"distance": distance}
		raise ValueError("""One and only one argument must be 0"""   )


# Run doctest
if __name__ == "__main__":
					import doctest

					doctest.testmod()










import unittest

import numpy as np







def        __lowerCamelCase (							__a       :np.ndarray   ,					__a       :np.ndarray   ,					__a       :np.ndarray   ,					__a       :np.ndarray | None = None   ,					)		->    np.ndarray:






		"""simple docstring"""

		A__  				=       np.shape(__a   )
		A__  				=       np.shape(__a   )
		A__  				=       np.shape(__a   )

		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(__a   )

		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(__a   )

		A__  				=       pseudo_inv
		if a_inv is None:
				try:
						A__  				=       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   A      (unittest.TestCase   ):
			'''simple docstring'''




			def        a_	(      self       :   Union[str, Any]       )     ->     None:







					"""simple docstring"""






					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(__lowerCAmelCase							,     __lowerCAmelCase							,     __lowerCAmelCase       )

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

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

					self.assertAlmostEqual(__lowerCAmelCase							,     det_a * det_s       )






			def        a_	(      self       :   str       )     ->     None:







					"""simple docstring"""






					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(__lowerCAmelCase       ):
							schur_complement(__lowerCAmelCase							,     __lowerCAmelCase							,     __lowerCAmelCase       )







			def        a_	(      self       :   List[str]       )     ->     None:







					"""simple docstring"""






					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(__lowerCAmelCase       ):
							schur_complement(__lowerCAmelCase							,     __lowerCAmelCase							,     __lowerCAmelCase       )


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					unittest.main()



