


from __future__ import annotations

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


def 			UpperCAmelCase_				(      UpperCAmelCase__						,							UpperCAmelCase__						,							UpperCAmelCase__						,							UpperCAmelCase__						,							):
					lowercase_  							=			coefficient_matrix.shape
					lowercase_  							=			constant_matrix.shape

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

					if colsa != 1:
										lowercase_  							=			F'''Constant matrix must be nx1 but received {rowsa}x{colsa}'''
										raise ValueError(SCREAMING_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(SCREAMING_SNAKE_CASE_  )

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

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

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

					lowercase_  							=			table.shape

					strictly_diagonally_dominant(SCREAMING_SNAKE_CASE_  )

					# Iterates the whole matrix for given number of times
					for _ in range(SCREAMING_SNAKE_CASE_  ):
										lowercase_  							=			[]
										for row in range(SCREAMING_SNAKE_CASE_  ):
															lowercase_  							=			0
															for col in range(SCREAMING_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(SCREAMING_SNAKE_CASE_  )
										lowercase_  							=			new_val

					return [float(SCREAMING_SNAKE_CASE_  ) for i in new_val]


def 			UpperCAmelCase_				(      UpperCAmelCase__  ):
					lowercase_  							=			table.shape

					lowercase_  							=			True

					for i in range(0						,							SCREAMING_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()



def 			UpperCAmelCase_				(      UpperCAmelCase__  ):
					if not isinstance(UpperCAmelCase__						,							UpperCAmelCase__  ):
										raise TypeError("""Input value must be an 'int' type"""  )

					lowercase_  							=			0
					while number:
										position += 1
										number >>= 1

					return position


if __name__ == "__main__":
							import doctest

							doctest.testmod()


