

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__       = (((515, 22, 13), 555), ((61, 35, 49), 150))
lowerCAmelCase__       = [2, 4, 1, 5]
lowerCAmelCase__       = len(train_data)
lowerCAmelCase__       = 0.0_0_9
def      _lowerCAmelCase(	__A   ,       __A="train"			):
  return calculate_hypothesis_value(__A   ,       __A			) - output(
      __A   ,       __A			)
def      _lowerCAmelCase(	__A			):
  UpperCAmelCase					      =  0
  for i in range(len(__A			) - 1			):
    hyp_val += data_input_tuple[i] * parameter_vector[i + 1]
  hyp_val += parameter_vector[0]
  return hyp_val
def      _lowerCAmelCase(	__A   ,       __A			):
  if data_set == "train":
    return train_data[example_no][1]
  elif data_set == "test":
    return test_data[example_no][1]
  return None
def      _lowerCAmelCase(	__A   ,       __A			):
  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(	__A   ,       __A=m			):
  UpperCAmelCase					      =  0
  for i in range(__A			):
    if index == -1:
      summation_value += _error(__A			)
    else:
      summation_value += _error(__A			) * train_data[i][0][index]
  return summation_value
def      _lowerCAmelCase(	__A			):
  UpperCAmelCase					      =  summation_of_cost_derivative(__A   ,       __A			) / m
  return cost_derivative_value
def      _lowerCAmelCase(	):
  global parameter_vector
  # Tune these values to set a tolerance value for predicted output
  UpperCAmelCase					      =  0.000002
  UpperCAmelCase					      =  0
  UpperCAmelCase					      =  0
  while True:
    j += 1
    UpperCAmelCase					      =  [0, 0, 0, 0]
    for i in range(0   ,       len(__A			)			):
      UpperCAmelCase					      =  get_cost_derivative(i - 1			)
      UpperCAmelCase					      =  (
          parameter_vector[i] - LEARNING_RATE * cost_derivative
      )
    if numpy.allclose(
        __A   ,       __A   ,       atol=__A   ,       rtol=__A   ,       ):
      break
    UpperCAmelCase					      =  temp_parameter_vector
  print(("Number of iterations:", j)			)
def      _lowerCAmelCase(	):
  for i in range(len(__A			)			):
    print(("Actual output value:", output(__A   ,       "test"			))			)
    print(("Hypothesis output:", calculate_hypothesis_value(__A   ,       "test"			))			)


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






def      _lowerCAmelCase(	__A   ,       __A			):
  return (pointa[0] - pointa[0]) ** 2 + (pointa[1] - pointa[1]) ** 2
def      _lowerCAmelCase(	__A   ,       __A=0			):
  return sorted(__A   ,       key=lambda __A			: x[column]			)
def      _lowerCAmelCase(	__A   ,       __A   ,       __A=float("inf"			)			):

  for i in range(points_counts - 1			):
    for j in range(i + 1   ,       __A			):
      UpperCAmelCase					      =  euclidean_distance_sqr(points[i]   ,       points[j]			)
      if current_dis < min_dis:
        UpperCAmelCase					      =  current_dis
  return min_dis
def      _lowerCAmelCase(	__A   ,       __A   ,       __A=float("inf"			)			):

  for i in range(min(6   ,       points_counts - 1			)   ,       __A			):
    for j in range(max(0   ,       i - 6			)   ,       __A			):
      UpperCAmelCase					      =  euclidean_distance_sqr(points[i]   ,       points[j]			)
      if current_dis < min_dis:
        UpperCAmelCase					      =  current_dis
  return min_dis
def      _lowerCAmelCase(	__A   ,       __A   ,       __A			):

  # base case
  if points_counts <= 3:
    return dis_between_closest_pair(__A   ,       __A			)

  # recursion
  UpperCAmelCase					      =  points_counts // 2
  UpperCAmelCase					      =  closest_pair_of_points_sqr(
      __A   ,       points_sorted_on_y[:mid]   ,       __A			)
  UpperCAmelCase					      =  closest_pair_of_points_sqr(
      __A   ,       points_sorted_on_y[mid:]   ,       points_counts - mid			)
  UpperCAmelCase					      =  min(__A   ,       __A			)
  UpperCAmelCase					      =  []
  for point in points_sorted_on_x:
    if abs(point[0] - points_sorted_on_x[mid][0]			) < closest_pair_dis:
      cross_strip.append(__A			)

  UpperCAmelCase					      =  dis_between_closest_in_strip(
      __A   ,       len(__A			)   ,       __A			)
  return min(__A   ,       __A			)
def      _lowerCAmelCase(	__A   ,       __A			):
  UpperCAmelCase					      =  column_based_sort(__A   ,       column=0			)
  UpperCAmelCase					      =  column_based_sort(__A   ,       column=1			)
  return (
      closest_pair_of_points_sqr(
          __A   ,       __A   ,       __A			)
  ) ** 0.5


if __name__ == "__main__":
      lowerCAmelCase__       = [(2, 3), (12, 30), (40, 50), (5, 1), (12, 10), (3, 4)]
      print("Distance:", closest_pair_of_points(points, len(points)))



