



'''simple docstring'''




import numpy

# List of input, output pairs
a   :			Any					  =    (
    ((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),
)
a   :			Optional[Any]					  =    (((5_1_5, 2_2, 1_3), 5_5_5), ((6_1, 3_5, 4_9), 1_5_0))
a   :			Tuple					  =    [2, 4, 1, 5]
a   :			List[str]					  =    len(train_data)
a   :			Union[str, Any]					  =    0.0_0_9



def       __lowerCamelCase  (					_lowercase	,				_lowercase="train"		)      ->			Tuple:
							return calculate_hypothesis_value(_lowerCAmelCase	,				_lowerCAmelCase		) - output(
							    _lowerCAmelCase	,				_lowerCAmelCase		)



def       __lowerCamelCase  (					_lowercase		)      ->			str:
							UpperCAmelCase     :		Dict							     =		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  (					_lowercase	,				_lowercase		)      ->			Any:
							if data_set == "train":
														return train_data[example_no][1]
							elif data_set == "test":
														return test_data[example_no][1]
							return None



def       __lowerCamelCase  (					_lowercase	,				_lowercase		)      ->			Tuple:
							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  (					_lowercase	,				_lowercase=m		)      ->			Any:
							UpperCAmelCase     :		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  (					_lowercase		)      ->			Any:
							UpperCAmelCase     :		str							     =		summation_of_cost_derivative(_lowerCAmelCase	,				_lowerCAmelCase		) / m
							return cost_derivative_value



def       __lowerCamelCase  (					)      ->			Union[str, Any]:
							global parameter_vector
							# Tune these values to set a tolerance value for predicted output
							UpperCAmelCase     :		int							     =		0.00_0002
							UpperCAmelCase     :		Optional[int]							     =		0
							UpperCAmelCase     :		List[str]							     =		0
							while True:
														j += 1
														UpperCAmelCase     :		List[Any]							     =		[0, 0, 0, 0]
														for i in range(0	,				len(_lowerCAmelCase		)		):
																					UpperCAmelCase     :		List[Any]							     =		get_cost_derivative(i - 1		)
																					UpperCAmelCase     :		Union[str, Any]							     =		(
																					    parameter_vector[i] - LEARNING_RATE * cost_derivative
																					)
														if numpy.allclose(
														    _lowerCAmelCase	,				_lowerCAmelCase	,				atol=_lowerCAmelCase	,				rtol=_lowerCAmelCase	,				):
																					break
														UpperCAmelCase     :		Union[str, Any]							     =		temp_parameter_vector
							print(("""Number of iterations:""", j)		)



def       __lowerCamelCase  (					)      ->			Tuple:
							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()








import functools



def 		A_				(     _lowerCAmelCase							,   _lowerCAmelCase     )						-> int:
 UpperCamelCase	:					Optional[int]       	=   len(_lowerCAmelCase     )
 UpperCamelCase	:					List[str]       	=   len(_lowerCAmelCase     )

 @functools.cache
 def min_distance(_lowerCAmelCase							,   _lowerCAmelCase     ) -> int:
  # if first word index is overflow - delete all from the second word
  if indexa >= len_worda:
   return len_worda - indexa
  # if second word index is overflow - delete all from the first word
  if indexa >= len_worda:
   return len_worda - indexa
  UpperCamelCase	:					Union[str, Any]       	=   int(worda[indexa] != worda[indexa]     )  # current letters not identical
  return min(
      1 + min_distance(indexa + 1							,   _lowerCAmelCase     )							,   1 + min_distance(_lowerCAmelCase							,   indexa + 1     )							,   diff + min_distance(indexa + 1							,   indexa + 1     )							,   )

 return min_distance(0							,   0     )


if __name__ == "__main__":
    import doctest

    doctest.testmod()
