






"""simple docstring"""






import numpy

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



def  __lowerCamelCase					(					lowerCAmelCase__       ,lowerCAmelCase__="train"				):
				return calculate_hypothesis_value(__UpperCAmelCase       ,__UpperCAmelCase				) - output(
				    __UpperCAmelCase       ,__UpperCAmelCase				)



def  __lowerCamelCase					(					lowerCAmelCase__				):
				A__							 =       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					(					lowerCAmelCase__       ,lowerCAmelCase__				):







				if data_set == "train":
								return train_data[example_no][1]
				elif data_set == "test":
								return test_data[example_no][1]
				return None



def  __lowerCamelCase					(					lowerCAmelCase__       ,lowerCAmelCase__				):







				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					(					lowerCAmelCase__       ,lowerCAmelCase__=m				):
				A__							 =       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					(					lowerCAmelCase__				):
				A__							 =       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__							 =       0.0_0_0_0_0_2
				A__							 =       0
				A__							 =       0
				while True:
								j += 1
								A__							 =       [0, 0, 0, 0]
								for i in range(0       ,len(__UpperCAmelCase				)				):
												A__							 =       get_cost_derivative(i - 1				)
												A__							 =       (
												    parameter_vector[i] - LEARNING_RATE * cost_derivative
												)
								if numpy.allclose(
								    __UpperCAmelCase       ,__UpperCAmelCase       ,atol=__UpperCAmelCase       ,rtol=__UpperCAmelCase       ,):
												break
								A__							 =       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()










"""simple docstring"""






class       snake_case_       :



	"""simple docstring"""

	def __init__(      self  ,					__a  ,					__a						):


					"""simple docstring"""

					A__							 =       name
					A__							 =       val


	def __str__(      self						):


					"""simple docstring"""

					return f'''{self.__class__.__name__}({self.name}, {self.val})'''






	def __lt__(      self  ,					__a						):


					"""simple docstring"""

					return self.val < other.val





class       snake_case_       :



	"""simple docstring"""

	def __init__(      self  ,					__a						):


					"""simple docstring"""

					A__							 =       {}
					A__							 =       {}
					A__							 =       self.build_heap(__a						)


	def __getitem__(      self  ,					__a						):


					"""simple docstring"""

					return self.get_value(__a						)


	def       _UpperCAmelCase						(      self  ,					__a						):


					"""simple docstring"""

					return (idx - 1) // 2


	def       _UpperCAmelCase						(      self  ,					__a						):


					"""simple docstring"""

					return idx * 2 + 1


	def       _UpperCAmelCase						(      self  ,					__a						):


					"""simple docstring"""

					return idx * 2 + 2


	def       _UpperCAmelCase						(      self  ,					__a						):


					"""simple docstring"""

					return self.heap_dict[key]


	def       _UpperCAmelCase						(      self  ,					__a						):


					"""simple docstring"""

					A__							 =       len(__a						) - 1
					A__							 =       self.get_parent_idx(__a						)

					for idx, i in enumerate(__a						):
									A__							 =       idx
									A__							 =       i.val

					for i in range(__a  ,					-1  ,					-1						):
									self.sift_down(__a  ,					__a						)
					return array


	def       _UpperCAmelCase						(      self  ,					__a  ,					__a						):


					"""simple docstring"""

					while True:
									A__							 =       self.get_left_child_idx(__a						)  # noqa: E741
									A__							 =       self.get_right_child_idx(__a						)

									A__							 =       idx
									if l < len(__a						) and array[l] < array[idx]:
													A__							 =       l
									if r < len(__a						) and array[r] < array[smallest]:
													A__							 =       r

									if smallest != idx:
													A__ ,			A__							 =       array[smallest], array[idx]
													(
													    (
													    A__
													) ,			(
													    A__
													) ,			
													)							 =       (
													    self.idx_of_element[array[smallest]],
													    self.idx_of_element[array[idx]],
													)
													A__							 =       smallest
									else:
													break


	def       _UpperCAmelCase						(      self  ,					__a						):


					"""simple docstring"""

					A__							 =       self.get_parent_idx(__a						)
					while p >= 0 and self.heap[p] > self.heap[idx]:
									A__ ,			A__							 =       self.heap[idx], self.heap[p]
									A__ ,			A__							 =       (
									    self.idx_of_element[self.heap[idx]],
									    self.idx_of_element[self.heap[p]],
									)
									A__							 =       p
									A__							 =       self.get_parent_idx(__a						)


	def       _UpperCAmelCase						(      self						):


					"""simple docstring"""

					return self.heap[0]


	def       _UpperCAmelCase						(      self						):


					"""simple docstring"""

					A__ ,			A__							 =       self.heap[-1], self.heap[0]
					A__ ,			A__							 =       (
					    self.idx_of_element[self.heap[-1]],
					    self.idx_of_element[self.heap[0]],
					)

					A__							 =       self.heap.pop()
					del self.idx_of_element[x]
					self.sift_down(0  ,					self.heap						)
					return x


	def       _UpperCAmelCase						(      self  ,					__a						):


					"""simple docstring"""

					self.heap.append(__a						)
					A__							 =       len(self.heap						) - 1
					A__							 =       node.val
					self.sift_up(len(self.heap						) - 1						)


	def       _UpperCAmelCase						(      self						):


					"""simple docstring"""

					return len(self.heap						) == 0






	def       _UpperCAmelCase						(      self  ,					__a  ,					__a						):


					"""simple docstring"""

					assert (
					    self.heap[self.idx_of_element[node]].val > new_value
					), "newValue must be less that current value"
					A__							 =       new_value
					A__							 =       new_value
					self.sift_up(self.idx_of_element[node]						)





SCREAMING_SNAKE_CASE						:						List[str]					   =       Node('''R''', -1)
SCREAMING_SNAKE_CASE						:						Tuple					   =       Node('''B''', 6)
SCREAMING_SNAKE_CASE						:						List[Any]					   =       Node('''A''', 3)
SCREAMING_SNAKE_CASE						:						int					   =       Node('''X''', 1)
SCREAMING_SNAKE_CASE						:						Union[str, Any]					   =       Node('''E''', 4)

# Use one of these two ways to generate Min-Heap

# Generating Min-Heap from array
SCREAMING_SNAKE_CASE						:						str					   =       MinHeap([r, b, a, x, e])

# Generating Min-Heap by Insert method
# myMinHeap.insert(a)
# myMinHeap.insert(b)
# myMinHeap.insert(x)
# myMinHeap.insert(r)
# myMinHeap.insert(e)

# Before
print('''Min Heap - before decrease key''')
for i in my_min_heap.heap:
					print(i)

print('''Min Heap - After decrease key of node [B -> -17]''')
my_min_heap.decrease_key(b, -17)

# After
for i in my_min_heap.heap:
					print(i)

if __name__ == "__main__":
					import doctest

					doctest.testmod()


