'''simple docstring'''




import unittest

import numpy as np




def 							lowerCamelCase			(   UpperCAmelCase__ :      np.ndarray   ,   UpperCAmelCase__ :      np.ndarray   ,   UpperCAmelCase__ :      np.ndarray   ,   UpperCAmelCase__ :      np.ndarray | None = None   ,   ):
							lowercase_      :    List[Any]       		= np.shape(UpperCAmelCase__				)
							lowercase_      :    Dict       		= np.shape(UpperCAmelCase__				)
							lowercase_      :    int       		= np.shape(UpperCAmelCase__				)

							if shape_a[0] != shape_b[0]:
														lowercase_      :    Optional[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(UpperCAmelCase__				)

							if shape_b[1] != shape_c[1]:
														lowercase_      :    Optional[Any]       		= (
														    """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(UpperCAmelCase__				)

							lowercase_      :    Any       		= pseudo_inv
							if a_inv is None:
														try:
																					lowercase_      :    List[str]       		= np.linalg.inv(UpperCAmelCase__				)
														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 			SCREAMING_SNAKE_CASE_  (			self       :						Optional[int]					):
										lowercase_      :    Tuple       		= np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]					)
										lowercase_      :    int       		= np.array([[0, 3], [3, 0], [2, 3]]					)
										lowercase_      :    Dict       		= np.array([[2, 1], [6, 3]]					)

										lowercase_      :    Union[str, Any]       		= schur_complement(lowercase_       ,    lowercase_       ,    lowercase_					)

										lowercase_      :    List[Any]       		= np.block([[a, b], [b.T, c]]					)

										lowercase_      :    Optional[int]       		= np.linalg.det(lowercase_					)
										lowercase_      :    int       		= np.linalg.det(lowercase_					)
										lowercase_      :    int       		= np.linalg.det(lowercase_					)

										self.assertAlmostEqual(lowercase_       ,    det_a * det_s					)







			def 			SCREAMING_SNAKE_CASE_  (			self       :						str					):
										lowercase_      :    int       		= np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]					)
										lowercase_      :    Optional[Any]       		= np.array([[0, 3], [3, 0], [2, 3]]					)
										lowercase_      :    Union[str, Any]       		= np.array([[2, 1], [6, 3]]					)

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







			def 			SCREAMING_SNAKE_CASE_  (			self       :						Any					):
										lowercase_      :    List[Any]       		= np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]					)
										lowercase_      :    List[Any]       		= np.array([[0, 3], [3, 0], [2, 3]]					)
										lowercase_      :    str       		= 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()






'''simple docstring'''




_lowercase		:				int	       =		"ABCDEFGHIJKLMNOPQRSTUVWXYZ"




def 							lowerCamelCase			(   )    ->   None:
							lowercase_      :    List[Any]       		= input("""Enter message: """				)
							lowercase_      :    str       		= input("""Enter key [alphanumeric]: """				)
							lowercase_      :    List[Any]       		= input("""Encrypt/Decrypt [e/d]: """				)

							if mode.lower().startswith("""e"""				):
														lowercase_      :    List[str]       		= """encrypt"""
														lowercase_      :    Optional[int]       		= encrypt_message(UpperCAmelCase__   ,   UpperCAmelCase__				)
							elif mode.lower().startswith("""d"""				):
														lowercase_      :    Any       		= """decrypt"""
														lowercase_      :    Optional[Any]       		= decrypt_message(UpperCAmelCase__   ,   UpperCAmelCase__				)

							print(F'''\n{mode.title()}ed message:'''				)
							print(UpperCAmelCase__				)




def 							lowerCamelCase			(   UpperCAmelCase__ :      str   ,   UpperCAmelCase__ :      str				)    ->   str:
							return translate_message(UpperCAmelCase__   ,   UpperCAmelCase__   ,   """encrypt"""				)




def 							lowerCamelCase			(   UpperCAmelCase__ :      str   ,   UpperCAmelCase__ :      str				)    ->   str:
							return translate_message(UpperCAmelCase__   ,   UpperCAmelCase__   ,   """decrypt"""				)




def 							lowerCamelCase			(   UpperCAmelCase__ :      str   ,   UpperCAmelCase__ :      str   ,   UpperCAmelCase__ :      str				)    ->   str:
							lowercase_      :    Union[str, Any]       		= []
							lowercase_      :    List[Any]       		= 0
							lowercase_      :    str       		= key.upper()

							for symbol in message:
														lowercase_      :    Tuple       		= LETTERS.find(symbol.upper()				)
														if num != -1:
																					if mode == "encrypt":
																												num += LETTERS.find(key[key_index]				)
																					elif mode == "decrypt":
																												num -= LETTERS.find(key[key_index]				)

																					num %= len(UpperCAmelCase__				)

																					if symbol.isupper():
																												translated.append(LETTERS[num]				)
																					elif symbol.islower():
																												translated.append(LETTERS[num].lower()				)

																					key_index += 1
																					if key_index == len(UpperCAmelCase__				):
																												lowercase_      :    Any       		= 0
														else:
																					translated.append(UpperCAmelCase__				)
							return "".join(UpperCAmelCase__				)


if __name__ == "__main__":
						main()





