




import numpy

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

def      A      (      _SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE="train"    )	-> str:
       return calculate_hypothesis_value(_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    ) - output(
           _SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )

def      A      (      _SCREAMING_SNAKE_CASE    )	-> List[str]:
       lowerCamelCase   :      Optional[Any]			 =					0
       for i in range(len(_SCREAMING_SNAKE_CASE    ) - 1    ):
              hyp_val += data_input_tuple[i] * parameter_vector[i + 1]
       hyp_val += parameter_vector[0]
       return hyp_val

def      A      (      _SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )	-> Optional[int]:
       if data_set == "train":
              return train_data[example_no][1]
       elif data_set == "test":
              return test_data[example_no][1]
       return None

def      A      (      _SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )	-> Union[str, Any]:
       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      A      (      _SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE=m    )	-> str:
       lowerCamelCase   :      List[Any]			 =					0
       for i in range(_SCREAMING_SNAKE_CASE    ):
              if index == -1:
                     summation_value += _error(_SCREAMING_SNAKE_CASE    )
              else:
                     summation_value += _error(_SCREAMING_SNAKE_CASE    ) * train_data[i][0][index]
       return summation_value

def      A      (      _SCREAMING_SNAKE_CASE    )	-> Tuple:
       lowerCamelCase   :      str			 =					summation_of_cost_derivative(_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    ) / m
       return cost_derivative_value

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

def      A      (      )	-> Dict:
       for i in range(len(_SCREAMING_SNAKE_CASE    )    ):
              print(("Actual output value:", output(_SCREAMING_SNAKE_CASE ,"test"    ))    )
              print(("Hypothesis output:", calculate_hypothesis_value(_SCREAMING_SNAKE_CASE ,"test"    ))    )


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












import random

def      A      (      _SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )	-> tuple:
       lowerCamelCase ,      lowerCamelCase ,      lowerCamelCase   :      Any			 =					[], [], []
       for element in data:
              if element < pivot:
                     less.append(_SCREAMING_SNAKE_CASE    )
              elif element > pivot:
                     greater.append(_SCREAMING_SNAKE_CASE    )
              else:
                     equal.append(_SCREAMING_SNAKE_CASE    )
       return less, equal, greater


def      A      (      _SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )	-> str:
       # index = len(items) // 2 when trying to find the median
       #   (value of index when items is sorted)

       # invalid input
       if index >= len(_SCREAMING_SNAKE_CASE    ) or index < 0:
              return None

       lowerCamelCase   :      List[Any]			 =					items[random.randint(0 ,len(_SCREAMING_SNAKE_CASE    ) - 1    )]
       lowerCamelCase   :      Dict			 =					0
       lowerCamelCase ,      lowerCamelCase ,      lowerCamelCase   :      Tuple			 =					_partition(_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )
       lowerCamelCase   :      Union[str, Any]			 =					len(_SCREAMING_SNAKE_CASE    )
       lowerCamelCase   :      str			 =					len(_SCREAMING_SNAKE_CASE    )

       # index is the pivot
       if m <= index < m + count:
              return pivot
       # must be in smaller
       elif m > index:
              return quick_select(_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )
       # must be in larger
       else:
              return quick_select(_SCREAMING_SNAKE_CASE ,index - (m + count)    )






