




import numpy

# List of input, output pairs
lowercase_	:				str  				= (
    ((5, 2, 3), 15),
    ((6, 5, 9), 25),
    ((11, 12, 13), 41),
    ((1, 1, 1), 8),
    ((11, 12, 13), 41),
)
lowercase_	:				Any  				= (((5_15, 22, 13), 5_55), ((61, 35, 49), 1_50))
lowercase_	:				Tuple  				= [2, 4, 1, 5]
lowercase_	:				Any  				= len(train_data)
lowercase_	:				Any  				= 0.0_09


def 							__SCREAMING_SNAKE_CASE  (			snake_case_	,    snake_case_="train"						):

						'''simple docstring'''


						return calculate_hypothesis_value(_lowercase	,    _lowercase						) - output(
						    _lowercase	,    _lowercase						)


def 							__SCREAMING_SNAKE_CASE  (			snake_case_						):

						'''simple docstring'''


						_UpperCAmelCase													=     0
						for i in range(len(_lowercase						) - 1						):
												hyp_val += data_input_tuple[i] * parameter_vector[i + 1]
						hyp_val += parameter_vector[0]
						return hyp_val


def 							__SCREAMING_SNAKE_CASE  (			snake_case_	,    snake_case_						):

						'''simple docstring'''


						if data_set == "train":
												return train_data[example_no][1]
						elif data_set == "test":
												return test_data[example_no][1]
						return None


def 							__SCREAMING_SNAKE_CASE  (			snake_case_	,    snake_case_						):

						'''simple docstring'''


						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 							__SCREAMING_SNAKE_CASE  (			snake_case_	,    snake_case_=m						):

						'''simple docstring'''


						_UpperCAmelCase													=     0
						for i in range(_lowercase						):
												if index == -1:
																		summation_value += _error(_lowercase						)
												else:
																		summation_value += _error(_lowercase						) * train_data[i][0][index]
						return summation_value


def 							__SCREAMING_SNAKE_CASE  (			snake_case_						):

						'''simple docstring'''


						_UpperCAmelCase													=     summation_of_cost_derivative(_lowercase	,    _lowercase						) / m
						return cost_derivative_value


def 							__SCREAMING_SNAKE_CASE  (			):

						'''simple docstring'''


						global parameter_vector
						# Tune these values to set a tolerance value for predicted output
						_UpperCAmelCase													=     0.000002
						_UpperCAmelCase													=     0
						_UpperCAmelCase													=     0
						while True:
												j += 1
												_UpperCAmelCase													=     [0, 0, 0, 0]
												for i in range(0	,    len(_lowercase						)						):
																		_UpperCAmelCase													=     get_cost_derivative(i - 1						)
																		_UpperCAmelCase													=     (
																		    parameter_vector[i] - LEARNING_RATE * cost_derivative
																		)
												if numpy.allclose(
												    _lowercase	,    _lowercase	,    atol=_lowercase	,    rtol=_lowercase	,    ):
																		break
												_UpperCAmelCase													=     temp_parameter_vector
						print(("Number of iterations:", j)						)


def 							__SCREAMING_SNAKE_CASE  (			):

						'''simple docstring'''


						for i in range(len(_lowercase						)						):
												print(("Actual output value:", output(_lowercase	,    "test"						))						)
												print(("Hypothesis output:", calculate_hypothesis_value(_lowercase	,    "test"						))						)


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









'''simple docstring'''




from itertools import count



def       __lowerCamelCase  (					_lowercase = 5_0		)      ->			int:
							UpperCAmelCase     :		Any							     =		[1] * min_block_length

							for n in count(_lowercase		):
														fill_count_functions.append(1		)

														for block_length in range(_lowercase	,				n + 1		):
																					for block_start in range(n - block_length		):
																												fill_count_functions[n] += fill_count_functions[
																												    n - block_start - block_length - 1
																												]

																					fill_count_functions[n] += 1

														if fill_count_functions[n] > 1_0_0_0_0_0_0:
																					break

							return n


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

