




import numpy

# List of input, output pairs
_snake_case            = (
    ((5, 2, 3), 15),
    ((6, 5, 9), 25),
    ((11, 12, 13), 41),
    ((1, 1, 1), 8),
    ((11, 12, 13), 41),
)
_snake_case            = (((515, 22, 13), 555), ((61, 35, 49), 150))
_snake_case            = [2, 4, 1, 5]
_snake_case            = len(train_data)
_snake_case            = 0.0_0_9







def        lowerCAmelCase_			(  snake_case_,snake_case_="train"  ):
						return calculate_hypothesis_value(_UpperCAmelCase,_UpperCAmelCase  ) - output(
						    _UpperCAmelCase,_UpperCAmelCase  )







def        lowerCAmelCase_			(  snake_case_  ):
						_A							:  int    =		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_			(  snake_case_,snake_case_  ):
						if data_set == "train":
												return train_data[example_no][1]
						elif data_set == "test":
												return test_data[example_no][1]
						return None







def        lowerCAmelCase_			(  snake_case_,snake_case_  ):
						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_			(  snake_case_,snake_case_=m  ):
						_A							:  List[str]    =		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_			(  snake_case_  ):
						_A							:  int    =		summation_of_cost_derivative(_UpperCAmelCase,_UpperCAmelCase  ) / m
						return cost_derivative_value







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







def        lowerCAmelCase_			(  ):
						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()







def        lowerCAmelCase_			(  snake_case_ = 1000000  ):
      _A							:  Any    =		limit + 1
      _A							:  Tuple    =		[0] * limit
      for first_term in range(1,snake_case_  ):
            for n in range(snake_case_,snake_case_,snake_case_  ):
                  _A							:  Optional[int]    =		first_term + n / first_term
                  if common_difference % 4:  # d must be divisble by 4
                        continue
                  else:
                        common_difference /= 4
                        if (
                            first_term > common_difference
                            and first_term < 4 * common_difference
                        ):  # since x,y,z are positive integers
                              frequency[n] += 1  # so z>0 and a>d ,also 4d<a

      _A							:  List[str]    =		sum(1 for x in frequency[1:limit] if x == 10  )

      return count


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

