


'''simple docstring'''






import numpy

# List of input, output pairs
__UpperCAmelCase       							=				(
    ((5, 2, 3), 15),
    ((6, 5, 9), 25),
    ((11, 12, 13), 41),
    ((1, 1, 1), 8),
    ((11, 12, 13), 41),
)
__UpperCAmelCase       							=				(((515, 22, 13), 555), ((61, 35, 49), 150))
__UpperCAmelCase       							=				[2, 4, 1, 5]
__UpperCAmelCase       							=				len(train_data)
__UpperCAmelCase       							=				0.009


def    _snake_case  (	A					,       A="train"			)		->       Optional[Any]:
							return calculate_hypothesis_value(A					,       A			) - output(
							    A					,       A			)


def    _snake_case  (	A			)		->       int:
							lowerCAmelCase__			  =      0
							for i in range(len(A			) - 1			):
														hyp_val += data_input_tuple[i] * parameter_vector[i + 1]
							hyp_val += parameter_vector[0]
							return hyp_val


def    _snake_case  (	A					,       A			)		->       List[Any]:
							if data_set == "train":
														return train_data[example_no][1]
							elif data_set == "test":
														return test_data[example_no][1]
							return None


def    _snake_case  (	A					,       A			)		->       int:
							if data_set == "train":
														return _hypothesis_value(train_data[example_no][0]			)
							elif data_set == "test":
														return _hypothesis_value(test_data[example_no][0]			)
							return None


def    _snake_case  (	A					,       A=m			)		->       Tuple:
							lowerCAmelCase__			  =      0
							for i in range(A			):
														if index == -1:
																					summation_value += _error(A			)
														else:
																					summation_value += _error(A			) * train_data[i][0][index]
							return summation_value


def    _snake_case  (	A			)		->       List[str]:
							lowerCAmelCase__			  =      summation_of_cost_derivative(A					,       A			) / m
							return cost_derivative_value


def    _snake_case  (	)		->       str:
							global parameter_vector
							# Tune these values to set a tolerance value for predicted output
							lowerCAmelCase__			  =      0.000_002
							lowerCAmelCase__			  =      0
							lowerCAmelCase__			  =      0
							while True:
														j += 1
														lowerCAmelCase__			  =      [0, 0, 0, 0]
														for i in range(0					,       len(A			)			):
																					lowerCAmelCase__			  =      get_cost_derivative(i - 1			)
																					lowerCAmelCase__			  =      (
																					    parameter_vector[i] - LEARNING_RATE * cost_derivative
																					)
														if numpy.allclose(
														    A					,       A					,       atol=A					,       rtol=A					,       ):
																					break
														lowerCAmelCase__			  =      temp_parameter_vector
							print(('''Number of iterations:''', j)			)


def    _snake_case  (	)		->       Union[str, Any]:
							for i in range(len(A			)			):
														print(('''Actual output value:''', output(A					,       '''test'''			))			)
														print(('''Hypothesis output:''', calculate_hypothesis_value(A					,       '''test'''			))			)


if __name__ == "__main__":
		run_gradient_descent()
		print('''\nTesting gradient descent for a linear hypothesis function.\n''')
		test_gradient_descent()



'''simple docstring'''






def    _snake_case  (	A					,       A			)		->       int:
							return x if y == 0 else greatest_common_divisor(A					,       x % y			)


def    _snake_case  (	A					,       A			)		->       int:
							return (x * y) // greatest_common_divisor(A					,       A			)


def    _snake_case  (	A = 20			)		->       int:
							lowerCAmelCase__			  =      1
							for i in range(1					,       n + 1			):
														lowerCAmelCase__			  =      lcm(A					,       A			)
							return g


if __name__ == "__main__":
		print(f"""{solution() = }""")