





import numpy

# List of input, output pairs
lowerCAmelCase_        =							(
    ((5, 2, 3), 1_5),
    ((6, 5, 9), 2_5),
    ((1_1, 1_2, 1_3), 4_1),
    ((1, 1, 1), 8),
    ((1_1, 1_2, 1_3), 4_1),
)
lowerCAmelCase_        =							(((5_1_5, 2_2, 1_3), 5_5_5), ((6_1, 3_5, 4_9), 1_5_0))
lowerCAmelCase_        =							[2, 4, 1, 5]
lowerCAmelCase_        =							len(train_data)
lowerCAmelCase_        =							0.009






def 	lowerCamelCase_		(							_UpperCamelCase					,							_UpperCamelCase="train"					)						->		List[str]:






				"""simple docstring"""


				return calculate_hypothesis_value(_UpperCamelCase					,							_UpperCamelCase					) - output(
				    _UpperCamelCase					,							_UpperCamelCase					)






def 	lowerCamelCase_		(							_UpperCamelCase					)						->		Union[str, Any]:






				"""simple docstring"""


				snake_case_		:       Optional[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_		(							_UpperCamelCase					,							_UpperCamelCase					)						->		Tuple:






				"""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 	lowerCamelCase_		(							_UpperCamelCase					,							_UpperCamelCase					)						->		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 	lowerCamelCase_		(							_UpperCamelCase					,							_UpperCamelCase=m					)						->		Union[str, Any]:






				"""simple docstring"""


				snake_case_		:       Union[str, Any]           =    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_		(							_UpperCamelCase					)						->		Union[str, Any]:






				"""simple docstring"""


				snake_case_		:       int           =    summation_of_cost_derivative(_UpperCamelCase					,							_UpperCamelCase					) / m
				return cost_derivative_value






def 	lowerCamelCase_		(							)						->		Tuple:






				"""simple docstring"""


				global parameter_vector
				# Tune these values to set a tolerance value for predicted output
				snake_case_		:       Optional[int]           =    0.000_002
				snake_case_		:       List[str]           =    0
				snake_case_		:       List[str]           =    0
				while True:
								j += 1
								snake_case_		:       str           =    [0, 0, 0, 0]
								for i in range(0					,							len(_UpperCamelCase					)					):
												snake_case_		:       str           =    get_cost_derivative(i - 1					)
												snake_case_		:       Any           =    (
												    parameter_vector[i] - LEARNING_RATE * cost_derivative
												)
								if numpy.allclose(
								    _UpperCamelCase					,							_UpperCamelCase					,							atol=_UpperCamelCase					,							rtol=_UpperCamelCase					,							):
												break
								snake_case_		:       Dict           =    temp_parameter_vector
				print(('''Number of iterations:''', j)					)






def 	lowerCamelCase_		(							)						->		int:






				"""simple docstring"""


				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()

"""simple docstring"""


def      __UpperCAmelCase       (      lowercase		):







  """simple docstring"""
  _UpperCAmelCase    			=   0
  _UpperCAmelCase    			=   len(lowercase		)

  for i in range(n - 1		):
    for j in range(i + 1 ,lowercase		):
      if arr[i] > arr[j]:
        num_inversions += 1

  return num_inversions






def      __UpperCAmelCase       (      lowercase		):







  """simple docstring"""
  if len(lowercase		) <= 1:
    return arr, 0
  _UpperCAmelCase    			=   len(lowercase		) // 2
  _UpperCAmelCase    			=   arr[0:mid]
  _UpperCAmelCase    			=   arr[mid:]

  _UpperCAmelCase			,					_UpperCAmelCase    			=   count_inversions_recursive(lowercase		)
  _UpperCAmelCase			,					_UpperCAmelCase    			=   count_inversions_recursive(lowercase		)
  _UpperCAmelCase			,					_UpperCAmelCase    			=   _count_cross_inversions(lowercase ,lowercase		)

  _UpperCAmelCase    			=   inversion_p + inversions_q + cross_inversions
  return c, num_inversions






def      __UpperCAmelCase       (      lowercase ,lowercase		):







  """simple docstring"""
  _UpperCAmelCase    			=   []
  _UpperCAmelCase    			=   _UpperCAmelCase    			=   _UpperCAmelCase    			=   0
  while i < len(lowercase		) and j < len(lowercase		):
    if p[i] > q[j]:
      # if P[1] > Q[j], then P[k] > Q[k] for all  i < k <= len(P)
      # These are all inversions. The claim emerges from the
      # property that P is sorted.
      num_inversion += len(lowercase		) - i
      r.append(q[j]		)
      j += 1
    else:
      r.append(p[i]		)
      i += 1

  if i < len(lowercase		):
    r.extend(p[i:]		)
  else:
    r.extend(q[j:]		)

  return r, num_inversion






def      __UpperCAmelCase       (      ):







  """simple docstring"""
  _UpperCAmelCase    			=   [10, 2, 1, 5, 5, 2, 11]

  # this arr has 8 inversions:
  # (10, 2), (10, 1), (10, 5), (10, 5), (10, 2), (2, 1), (5, 2), (5, 2)

  _UpperCAmelCase    			=   count_inversions_bf(lowercase		)
  _UpperCAmelCase			,					_UpperCAmelCase    			=   count_inversions_recursive(lowercase		)

  assert num_inversions_bf == num_inversions_recursive == 8

  print("""number of inversions = """ ,lowercase		)

  # testing an array with zero inversion (a sorted arr_1)

  arr_a.sort()
  _UpperCAmelCase    			=   count_inversions_bf(lowercase		)
  _UpperCAmelCase			,					_UpperCAmelCase    			=   count_inversions_recursive(lowercase		)

  assert num_inversions_bf == num_inversions_recursive == 0
  print("""number of inversions = """ ,lowercase		)

  # an empty list should also have zero inversions
  _UpperCAmelCase    			=   []
  _UpperCAmelCase    			=   count_inversions_bf(lowercase		)
  _UpperCAmelCase			,					_UpperCAmelCase    			=   count_inversions_recursive(lowercase		)

  assert num_inversions_bf == num_inversions_recursive == 0
  print("""number of inversions = """ ,lowercase		)


if __name__ == "__main__":
    main()
