





from __future__ import annotations

import math
def      _A       (		SCREAMING_SNAKE_CASE     :   int						):





  """simple docstring"""



  if 1 < number < 4:
    # 2 and 3 are primes
    return True
  elif number < 2 or number % 2 == 0 or number % 3 == 0:
    # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
    return False

  # All primes number are in format of 6k +/- 1
  for i in range(5       ,       int(math.sqrt(SCREAMING_SNAKE_CASE						) + 1						)       ,       6						):
    if number % i == 0 or number % (i + 2) == 0:
      return False
  return True


UpperCAmelCase	:	Dict		     =       [num for num in range(3, 100001, 2) if not is_prime(num)]
def      _A       (		SCREAMING_SNAKE_CASE     :   int						):





  """simple docstring"""



  if not isinstance(SCREAMING_SNAKE_CASE       ,       SCREAMING_SNAKE_CASE						):
    raise ValueError("n must be an integer"						)
  if n <= 0:
    raise ValueError("n must be >= 0"						)

  a__	:					List[Any]										=[]
  for num in range(len(SCREAMING_SNAKE_CASE						)						):
    a__	:					int										=0
    while 2 * i * i <= odd_composites[num]:
      a__	:					Optional[Any]										=odd_composites[num] - 2 * i * i
      if is_prime(SCREAMING_SNAKE_CASE						):
        break
      i += 1
    else:
      list_nums.append(odd_composites[num]						)
      if len(SCREAMING_SNAKE_CASE						) == n:
        return list_nums

  return []
def      _A       (		):





  """simple docstring"""



  return compute_nums(1						)[0]


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













import numpy

# List of input, output pairs
UpperCAmelCase	:	str		     =       (
    ((5, 2, 3), 15),
    ((6, 5, 9), 25),
    ((11, 12, 13), 41),
    ((1, 1, 1), 8),
    ((11, 12, 13), 41),
)
UpperCAmelCase	:	Optional[int]		     =       (((515, 22, 13), 555), ((61, 35, 49), 150))
UpperCAmelCase	:	str		     =       [2, 4, 1, 5]
UpperCAmelCase	:	List[str]		     =       len(train_data)
UpperCAmelCase	:	Dict		     =       0.0_0_9
def      _A       (		SCREAMING_SNAKE_CASE     :   Tuple       ,       SCREAMING_SNAKE_CASE     :   Tuple="train"						):





  """simple docstring"""



  return calculate_hypothesis_value(SCREAMING_SNAKE_CASE       ,       SCREAMING_SNAKE_CASE						) - output(
      SCREAMING_SNAKE_CASE       ,       SCREAMING_SNAKE_CASE						)
def      _A       (		SCREAMING_SNAKE_CASE     :   Tuple						):





  """simple docstring"""



  a__	:					Tuple										=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     :   Dict       ,       SCREAMING_SNAKE_CASE     :   Dict						):





  """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      _A       (		SCREAMING_SNAKE_CASE     :   Optional[Any]       ,       SCREAMING_SNAKE_CASE     :   Tuple						):





  """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      _A       (		SCREAMING_SNAKE_CASE     :   Union[str, Any]       ,       SCREAMING_SNAKE_CASE     :   int=m						):





  """simple docstring"""



  a__	:					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     :   int						):





  """simple docstring"""



  a__	:					Any										=summation_of_cost_derivative(SCREAMING_SNAKE_CASE       ,       SCREAMING_SNAKE_CASE						) / m
  return cost_derivative_value
def      _A       (		):





  """simple docstring"""



  global parameter_vector
  # Tune these values to set a tolerance value for predicted output
  a__	:					Dict										=0.0_0_0_0_0_2
  a__	:					Union[str, Any]										=0
  a__	:					Any										=0
  while True:
    j += 1
    a__	:					Any										=[0, 0, 0, 0]
    for i in range(0       ,       len(SCREAMING_SNAKE_CASE						)						):
      a__	:					Tuple										=get_cost_derivative(i - 1						)
      a__	:					List[Any]										=(
          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
    a__	:					Optional[Any]										=temp_parameter_vector
  print(("Number of iterations:", j)						)
def      _A       (		):





  """simple docstring"""



  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()






