from __future__ import annotations

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





def 				UpperCAmelCase						(    lowercase							,			lowercase							,			lowercase							,			lowercase							,			):







				"""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(__lowerCamelCase							)

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

				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(__lowerCamelCase							)

				if len(__lowerCamelCase							) != rowsa:
								__lowercase 			=							(
								    '''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 			=							np.concatenate(
				    (coefficient_matrix, constant_matrix)							,			axis=1							)

				__lowercase			,     __lowercase 			=							table.shape

				strictly_diagonally_dominant(__lowerCamelCase							)

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

				return [float(__lowerCamelCase							) for i in new_val]





def 				UpperCAmelCase						(    lowercase							):







				"""simple docstring"""



				__lowercase			,     __lowercase 			=							table.shape

				__lowercase 			=							True

				for i in range(0							,			__lowerCamelCase							):
								__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()





from math import pi, sqrt





def 		__A		(	__lowerCamelCase    )      ->       float:
	if num <= 0:
		raise ValueError("""math domain error"""    )
	if num > 171.5:
		raise OverflowError("""math range error"""    )
	elif num - int(__lowerCamelCase    ) not in (0, 0.5):
		raise NotImplementedError("""num must be an integer or a half-integer"""    )
	elif num == 0.5:
		return sqrt(__lowerCamelCase    )
	else:
		return 1.0 if num == 1 else (num - 1) * gamma(num - 1    )





def 		__A		(	)      ->       None:
	assert gamma(0.5    ) == sqrt(__lowerCamelCase    )
	assert gamma(1    ) == 1.0
	assert gamma(2    ) == 1.0


if __name__ == "__main__":
		from doctest import testmod

		testmod()
		__UpperCamelCase					:       str    					=      1.0
		while num:
				__UpperCamelCase					:       Dict    					=      float(input("Gamma of: "))
				print(F'gamma({num}) = {gamma(num)}')
				print("\nEnter 0 to exit...")

