



import numpy

# List of input, output pairs
lowerCAmelCase__					  =  (
    ((5, 2, 3), 1_5),
    ((6, 5, 9), 2_5),
    ((1_1, 1_2, 1_3), 4_1),
    ((1, 1, 1), 8),
    ((1_1, 1_2, 1_3), 4_1),
)
lowerCAmelCase__					  =  (((5_1_5, 2_2, 1_3), 5_5_5), ((6_1, 3_5, 4_9), 1_5_0))
lowerCAmelCase__					  =  [2, 4, 1, 5]
lowerCAmelCase__					  =  len(train_data)
lowerCAmelCase__					  =  0.009


def  __lowerCamelCase (       lowerCamelCase__					,			lowerCamelCase__="train"						):

				"""simple docstring"""


				return calculate_hypothesis_value(lowerCamelCase__					,			lowerCamelCase__						) - output(
				    lowerCamelCase__					,			lowerCamelCase__						)


def  __lowerCamelCase (       lowerCamelCase__						):

				"""simple docstring"""


				lowercase__					:   List[Any]													=					0
				for i in range(len(lowerCamelCase__						) - 1						):
								hyp_val += data_input_tuple[i] * parameter_vector[i + 1]
				hyp_val += parameter_vector[0]
				return hyp_val


def  __lowerCamelCase (       lowerCamelCase__					,			lowerCamelCase__						):

				"""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  __lowerCamelCase (       lowerCamelCase__					,			lowerCamelCase__						):

				"""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  __lowerCamelCase (       lowerCamelCase__					,			lowerCamelCase__=m						):

				"""simple docstring"""


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


def  __lowerCamelCase (       lowerCamelCase__						):

				"""simple docstring"""


				lowercase__					:   Union[str, Any]													=					summation_of_cost_derivative(lowerCamelCase__					,			lowerCamelCase__						) / m
				return cost_derivative_value


def  __lowerCamelCase (       ):

				"""simple docstring"""


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


def  __lowerCamelCase (       ):

				"""simple docstring"""


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


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









def  __lowerCamelCase (       lowerCamelCase__ = 1_000						):

				"""simple docstring"""


				lowercase__							,							lowercase__					:   int													=					1, 1
				lowercase__					:   List[Any]													=					[]
				for i in range(1					,			n + 1						):
								lowercase__					:   Dict													=					prev_numerator + 2 * prev_denominator
								lowercase__					:   Tuple													=					prev_numerator + prev_denominator
								if len(str(lowerCamelCase__						)						) > len(str(lowerCamelCase__						)						):
												result.append(lowerCamelCase__						)
								lowercase__					:   int													=					numerator
								lowercase__					:   int													=					denominator

				return len(lowerCamelCase__						)


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




