




from string import ascii_uppercase

__A   :  Dict					=      {char: i for i, char in enumerate(ascii_uppercase)}
__A   :  Tuple					=      dict(enumerate(ascii_uppercase))

def 						snake_case__       (					_lowerCamelCase,  _lowerCamelCase				)			->str:






		"""simple docstring"""


		__lowercase				:		int												=				len(_lowerCamelCase				)
		__lowercase				:		Tuple												=				0
		while True:
				if x == i:
						__lowercase				:		Optional[int]												=				0
				if len(_lowerCamelCase				) == len(_lowerCamelCase				):
						break
				key += key[i]
				i += 1
		return key

def 						snake_case__       (					_lowerCamelCase,  _lowerCamelCase				)			->str:






		"""simple docstring"""


		__lowercase				:		List[str]												=				""
		__lowercase				:		int												=				0
		for letter in message:
				if letter == " ":
						cipher_text += " "
				else:
						__lowercase				:		int												=				(dicta[letter] - dicta[key_new[i]]) % 26
						i += 1
						cipher_text += dicta[x]
		return cipher_text

def 						snake_case__       (					_lowerCamelCase,  _lowerCamelCase				)			->str:






		"""simple docstring"""


		__lowercase				:		Any												=				""
		__lowercase				:		Any												=				0
		for letter in cipher_text:
				if letter == " ":
						or_txt += " "
				else:
						__lowercase				:		Dict												=				(dicta[letter] + dicta[key_new[i]] + 26) % 26
						i += 1
						or_txt += dicta[x]
		return or_txt

def 						snake_case__       (					)			->None:






		"""simple docstring"""


		__lowercase				:		Optional[int]												=				"THE GERMAN ATTACK"
		__lowercase				:		Optional[int]												=				"SECRET"
		__lowercase				:		Optional[Any]												=				generate_key(_lowerCamelCase,  _lowerCamelCase				)
		__lowercase				:		Optional[Any]												=				cipher_text(_lowerCamelCase,  _lowerCamelCase				)
		print(F'Encrypted Text = {s}'				)
		print(F'Original Text = {original_text(_lowerCamelCase,  _lowerCamelCase				)}'				)


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						main()






"""simple docstring"""







from __future__ import annotations

import numpy as np
from numpy import floataa
from numpy.typing import NDArray

def 						snake_case__       (					_lowerCamelCase,  _lowerCamelCase,  _lowerCamelCase,  _lowerCamelCase,  )			->list[float]:






		"""simple docstring"""


		__lowercase						,__lowercase				:		Dict												=				coefficient_matrix.shape
		__lowercase						,__lowercase				:		Tuple												=				constant_matrix.shape

		if rowsa != colsa:
				__lowercase				:		str												=				F'Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}'
				raise ValueError(_lowerCamelCase				)

		if colsa != 1:
				__lowercase				:		Dict												=				F'Constant matrix must be nx1 but received {rowsa}x{colsa}'
				raise ValueError(_lowerCamelCase				)

		if rowsa != rowsa:
				__lowercase				:		Optional[Any]												=				(
				    "Coefficient and constant matrices dimensions must be nxn and nx1 but "
				    F'received {rowsa}x{colsa} and {rowsa}x{colsa}'
				)
				raise ValueError(_lowerCamelCase				)

		if len(_lowerCamelCase				) != rowsa:
				__lowercase				:		Dict												=				(
				    "Number of initial values must be equal to number of rows in coefficient "
				    F'matrix but received {len(_lowerCamelCase				)} and {rowsa}'
				)
				raise ValueError(_lowerCamelCase				)

		if iterations <= 0:
				raise ValueError("Iterations must be at least 1"				)

		__lowercase				:		NDArray[floataa]												=				np.concatenate(
		    (coefficient_matrix, constant_matrix),  axis=1				)

		__lowercase						,__lowercase				:		str												=				table.shape

		strictly_diagonally_dominant(_lowerCamelCase				)

		# Iterates the whole matrix for given number of times
		for _ in range(_lowerCamelCase				):
				__lowercase				:		List[Any]												=				[]
				for row in range(_lowerCamelCase				):
						__lowercase				:		Optional[Any]												=				0
						for col in range(_lowerCamelCase				):
								if col == row:
										__lowercase				:		Tuple												=				table[row][col]
								elif col == cols - 1:
										__lowercase				:		Tuple												=				table[row][col]
								else:
										temp += (-1) * table[row][col] * init_val[col]
						__lowercase				:		List[Any]												=				(temp + val) / denom
						new_val.append(_lowerCamelCase				)
				__lowercase				:		Dict												=				new_val

		return [float(_lowerCamelCase				) for i in new_val]

def 						snake_case__       (					_lowerCamelCase				)			->bool:






		"""simple docstring"""


		__lowercase						,__lowercase				:		int												=				table.shape

		__lowercase				:		Optional[int]												=				True

		for i in range(0,  _lowerCamelCase				):
				__lowercase				:		Optional[int]												=				0
				for j in range(0,  cols - 1				):
						if i == j:
								continue
						else:
								total += table[i][j]

				if table[i][i] <= total:
						raise ValueError("Coefficient matrix is not strictly diagonally dominant"				)

		return is_diagonally_dominant


# Test Cases
if __name__ == "__main__":
						import doctest

						doctest.testmod()
