


from __future__ import annotations

import numpy as np
from numpy import floataa
from numpy.typing import NDArray
def 			_a (      SCREAMING_SNAKE_CASE						,				SCREAMING_SNAKE_CASE						,				SCREAMING_SNAKE_CASE						,				SCREAMING_SNAKE_CASE						,				):


		"""simple docstring"""




		lowercase__     ,		lowercase__            =      coefficient_matrix.shape
		lowercase__     ,		lowercase__            =      constant_matrix.shape

		if rowsa != colsa:
				lowercase__            =      f'Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}'
				raise ValueError(snake_case__     )

		if colsa != 1:
				lowercase__            =      f'Constant matrix must be nx1 but received {rowsa}x{colsa}'
				raise ValueError(snake_case__     )

		if rowsa != rowsa:
				lowercase__            =      (
				    '''Coefficient and constant matrices dimensions must be nxn and nx1 but '''
				    f'received {rowsa}x{colsa} and {rowsa}x{colsa}'
				)
				raise ValueError(snake_case__     )

		if len(snake_case__     ) != rowsa:
				lowercase__            =      (
				    '''Number of initial values must be equal to number of rows in coefficient '''
				    f'matrix but received {len(snake_case__     )} and {rowsa}'
				)
				raise ValueError(snake_case__     )

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

		lowercase__            =      np.concatenate(
		    (coefficient_matrix, constant_matrix)						,				axis=1     )

		lowercase__     ,		lowercase__            =      table.shape

		strictly_diagonally_dominant(snake_case__     )

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

		return [float(snake_case__     ) for i in new_val]
def 			_a (      SCREAMING_SNAKE_CASE     ):


		"""simple docstring"""




		lowercase__     ,		lowercase__            =      table.shape

		lowercase__            =      True

		for i in range(0						,				snake_case__     ):
				lowercase__            =      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()








"""simple docstring"""




from __future__ import annotations



def     a__ (				snake_case__       , snake_case__				)						->					bool:
			if len(snake_case__				) == 0:
						return False
			lowerCamelCase			      =					len(snake_case__				) // 2
			if a_list[midpoint] == item:
						return True
			if item < a_list[midpoint]:
						return binary_search(a_list[:midpoint]       , snake_case__				)
			else:
						return binary_search(a_list[midpoint + 1 :]       , snake_case__				)


if __name__ == "__main__":
					lowerCAmelCase							:			List[Any]     							=							input("""Enter numbers separated by comma:\n""").strip()
					lowerCAmelCase							:			Optional[Any]     							=							[int(item.strip()) for item in user_input.split(""",""")]
					lowerCAmelCase							:			Optional[int]     							=							int(input("""Enter the number to be found in the list:\n""").strip())
					lowerCAmelCase							:			Union[str, Any]     							=							"""""" if binary_search(sequence, target) else """not """
					print(F"""{target} was {not_str}found in {sequence}""")



