


import numpy

# List of input, output pairs
lowerCAmelCase__      		= (
    ((5, 2, 3), 15),
    ((6, 5, 9), 25),
    ((11, 12, 13), 41),
    ((1, 1, 1), 8),
    ((11, 12, 13), 41),
)
lowerCAmelCase__      		= (((5_15, 22, 13), 5_55), ((61, 35, 49), 1_50))
lowerCAmelCase__      		= [2, 4, 1, 5]
lowerCAmelCase__      		= len(train_data)
lowerCAmelCase__      		= 0.0_09
def 							_UpperCAmelCase				(UpperCamelCase__     :  Optional[int]				,							UpperCamelCase__     :  Any="train"						):
       return calculate_hypothesis_value(lowerCamelCase__				,							lowerCamelCase__						) - output(
           lowerCamelCase__				,							lowerCamelCase__						)
def 							_UpperCAmelCase				(UpperCamelCase__     :  int						):
       _A      :       int				    = 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 							_UpperCAmelCase				(UpperCamelCase__     :  Dict				,							UpperCamelCase__     :  Union[str, Any]						):
       if data_set == "train":
              return train_data[example_no][1]
       elif data_set == "test":
              return test_data[example_no][1]
       return None
def 							_UpperCAmelCase				(UpperCamelCase__     :  List[str]				,							UpperCamelCase__     :  List[str]						):
       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 							_UpperCAmelCase				(UpperCamelCase__     :  List[Any]				,							UpperCamelCase__     :  Union[str, Any]=m						):
       _A      :       Any				    = 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 							_UpperCAmelCase				(UpperCamelCase__     :  Optional[int]						):
       _A      :       Optional[int]				    = summation_of_cost_derivative(lowerCamelCase__				,							lowerCamelCase__						) / m
       return cost_derivative_value
def 							_UpperCAmelCase				():
       global parameter_vector
       # Tune these values to set a tolerance value for predicted output
       _A      :       Optional[int]				    = 0.00_00_02
       _A      :       Union[str, Any]				    = 0
       _A      :       List[str]				    = 0
       while True:
              j += 1
              _A      :       Optional[int]				    = [0, 0, 0, 0]
              for i in range(0				,							len(lowerCamelCase__						)						):
                     _A      :       int				    = get_cost_derivative(i - 1						)
                     _A      :       List[Any]				    = (
                         parameter_vector[i] - LEARNING_RATE * cost_derivative
                     )
              if numpy.allclose(
                  lowerCamelCase__				,							lowerCamelCase__				,							atol=lowerCamelCase__				,							rtol=lowerCamelCase__				,							):
                     break
              _A      :       Optional[int]				    = temp_parameter_vector
       print(("Number of iterations:", j)						)
def 							_UpperCAmelCase				():
       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__	, lowerCamelCase__    ):
				lowerCamelCase_						=			[0 for i in range(r + 1    )]
				# nc0 = 1
				lowerCamelCase_						=			1
				for i in range(1	, n + 1    ):
								# to compute current row from previous row.
								lowerCamelCase_						=			min(lowerCamelCase__	, lowerCamelCase__    )
								while j > 0:
												c[j] += c[j - 1]
												j -= 1
				return c[r]





print(binomial_coefficient(n=1_0, r=5))


