

"""simple docstring"""





def   _A  (  UpperCamelCase_     :       list,			UpperCamelCase_     :       list)	->						float:
   '''simple docstring'''


   _validate_point(UpperCamelCase_)
   _validate_point(UpperCamelCase_)
   if len(UpperCamelCase_) != len(UpperCamelCase_):
      raise ValueError("Both points must be in the same n-dimensional space")

   return float(sum(abs(a - b) for a, b in zip(UpperCamelCase_,			UpperCamelCase_)))




def   _A  (  UpperCamelCase_     :       list[float])	->						None:
   '''simple docstring'''


   if point:
      if isinstance(UpperCamelCase_,			UpperCamelCase_):
         for item in point:
            if not isinstance(UpperCamelCase_,			(int, float)):
               __lowercase								=						(
                   "Expected a list of numbers as input, found "
                   F"""{type(UpperCamelCase_).__name__}"""
               )
               raise TypeError(UpperCamelCase_)
      else:
         __lowercase								=						F"""Expected a list of numbers as input, found {type(UpperCamelCase_).__name__}"""
         raise TypeError(UpperCamelCase_)
   else:
      raise ValueError("Missing an input")




def   _A  (  UpperCamelCase_     :       list,			UpperCamelCase_     :       list)	->						float:
   '''simple docstring'''


   _validate_point(UpperCamelCase_)
   _validate_point(UpperCamelCase_)
   if len(UpperCamelCase_) != len(UpperCamelCase_):
      raise ValueError("Both points must be in the same n-dimensional space")

   return float(sum(abs(x - y) for x, y in zip(UpperCamelCase_,			UpperCamelCase_)))


if __name__ == "__main__":
   import doctest

   doctest.testmod()








"""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     :   str			    =			(((5_1_5, 2_2, 1_3), 5_5_5), ((6_1, 3_5, 4_9), 1_5_0))
A     :   Union[str, Any]			    =			[2, 4, 1, 5]
A     :   int			    =			len(train_data)
A     :   Dict			    =			0.009


def _lowerCamelCase	(		_UpperCamelCase    , _UpperCamelCase="train"      ):

			'''simple docstring'''




			return calculate_hypothesis_value(_UpperCamelCase    , _UpperCamelCase      ) - output(
			    _UpperCamelCase    , _UpperCamelCase      )


def _lowerCamelCase	(		_UpperCamelCase      ):

			'''simple docstring'''




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


def _lowerCamelCase	(		_UpperCamelCase    , _UpperCamelCase      ):

			'''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	(		_UpperCamelCase    , _UpperCamelCase      ):

			'''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	(		_UpperCamelCase    , _UpperCamelCase=m      ):

			'''simple docstring'''




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


def _lowerCamelCase	(		_UpperCamelCase      ):

			'''simple docstring'''




			__lowerCAmelCase				    =			summation_of_cost_derivative(_UpperCamelCase    , _UpperCamelCase      ) / m
			return cost_derivative_value


def _lowerCamelCase	(		):

			'''simple docstring'''




			global parameter_vector
			# Tune these values to set a tolerance value for predicted output
			__lowerCAmelCase				    =			0.00_00_02
			__lowerCAmelCase				    =			0
			__lowerCAmelCase				    =			0
			while True:
						j += 1
						__lowerCAmelCase				    =			[0, 0, 0, 0]
						for i in range(0    , len(_UpperCamelCase      )      ):
									__lowerCAmelCase				    =			get_cost_derivative(i - 1      )
									__lowerCAmelCase				    =			(
									    parameter_vector[i] - LEARNING_RATE * cost_derivative
									)
						if numpy.allclose(
						    _UpperCamelCase    , _UpperCamelCase    , atol=_UpperCamelCase    , rtol=_UpperCamelCase    , ):
									break
						__lowerCAmelCase				    =			temp_parameter_vector
			print(("Number of iterations:", j)      )


def _lowerCamelCase	(		):

			'''simple docstring'''




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


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




