


"""simple docstring"""




from __future__ import annotations

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





def       a_ (	lowercase__ :NDArray[floataa],			lowercase__ :NDArray[floataa],			lowercase__ :list[int],			lowercase__ :int,			):
			__lowerCamelCase     ,__lowerCamelCase          =      coefficient_matrix.shape
			__lowerCamelCase     ,__lowerCamelCase          =      constant_matrix.shape

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

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

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

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

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

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

			__lowerCamelCase     ,__lowerCamelCase          =      table.shape

			strictly_diagonally_dominant(lowercase__     )

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

			return [float(lowercase__     ) for i in new_val]





def       a_ (	lowercase__ :NDArray[floataa]     ):
			__lowerCamelCase     ,__lowerCamelCase          =      table.shape

			__lowerCamelCase          =      True

			for i in range(0,			lowercase__     ):
						__lowerCamelCase          =      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_ (	lowercase__ :list[float]     ):
			if len(lowercase__     ) < 2:
						raise ValueError("""Monogons and Digons are not polygons in the Euclidean space"""     )
			if any(i <= 0 for i in nums     ):
						raise ValueError("""All values must be greater than 0"""     )
			__lowerCamelCase          =      nums.copy()
			copy_nums.sort()
			return copy_nums[-1] < sum(copy_nums[:-1]     )


if __name__ == "__main__":
					import doctest

					doctest.testmod()




