


_snake_case  :	int			      =       {
    "a": "AAAAA",
    "b": "AAAAB",
    "c": "AAABA",
    "d": "AAABB",
    "e": "AABAA",
    "f": "AABAB",
    "g": "AABBA",
    "h": "AABBB",
    "i": "ABAAA",
    "j": "BBBAA",
    "k": "ABAAB",
    "l": "ABABA",
    "m": "ABABB",
    "n": "ABBAA",
    "o": "ABBAB",
    "p": "ABBBA",
    "q": "ABBBB",
    "r": "BAAAA",
    "s": "BAAAB",
    "t": "BAABA",
    "u": "BAABB",
    "v": "BBBAB",
    "w": "BABAA",
    "x": "BABAB",
    "y": "BABBA",
    "z": "BABBB",
    " ": " ",
}


_snake_case  :	Optional[Any]			      =       {value: key for key, value in encode_dict.items()}







def        lowerCAmelCase_  (      __lowerCamelCase			):
							__snake_case	:    Union[str, Any]											=     ""
							for letter in word.lower():
														if letter.isalpha() or letter == " ":
																					encoded += encode_dict[letter]
														else:
																					raise Exception("encode() accepts only letters of the alphabet and spaces"			)
							return encoded







def        lowerCAmelCase_  (      __lowerCamelCase			):
							if set(__lowerCamelCase			) - {"A", "B", " "} != set():
														raise Exception("decode() accepts only 'A', 'B' and spaces"			)
							__snake_case	:    Union[str, Any]											=     ""
							for word in coded.split():
														while len(__lowerCamelCase			) != 0:
																					decoded += decode_dict[word[:5]]
																					__snake_case	:    Any											=     word[5:]
														decoded += " "
							return decoded.strip()


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

			testmod()





import unittest

import numpy as np







def        lowerCAmelCase_  (      __lowerCamelCase							,			__lowerCamelCase							,			__lowerCamelCase							,			__lowerCamelCase = None							,			):
							__snake_case	:    List[str]											=     np.shape(__lowerCamelCase			)
							__snake_case	:    Optional[Any]											=     np.shape(__lowerCamelCase			)
							__snake_case	:    List[str]											=     np.shape(__lowerCamelCase			)

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

							__snake_case	:    str											=     pseudo_inv
							if a_inv is None:
														try:
																					__snake_case	:    Optional[Any]											=     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        a	(unittest.TestCase   ):




							"""simple docstring"""


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

														__snake_case	:    Dict											=     schur_complement(lowerCamelCase					,			lowerCamelCase					,			lowerCamelCase       )

														__snake_case	:    int											=     np.block([[a, b], [b.T, c]]       )

														__snake_case	:    Optional[int]											=     np.linalg.det(lowerCamelCase       )
														__snake_case	:    Any											=     np.linalg.det(lowerCamelCase       )
														__snake_case	:    Tuple											=     np.linalg.det(lowerCamelCase       )

														self.assertAlmostEqual(lowerCamelCase					,			det_a * det_s       )

							def 					__snake_case      (							self :						int       )			->					None:
														__snake_case	:    str											=     np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]       )
														__snake_case	:    Dict											=     np.array([[0, 3], [3, 0], [2, 3]]       )
														__snake_case	:    Tuple											=     np.array([[2, 1], [6, 3]]       )

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






							def 					__snake_case      (							self :						List[Any]       )			->					None:
														__snake_case	:    List[Any]											=     np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]       )
														__snake_case	:    Tuple											=     np.array([[0, 3], [3, 0], [2, 3]]       )
														__snake_case	:    List[Any]											=     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()

