



import numpy

# List of input, output pairs
a_						:     Optional[Any]	     =		(
    ((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),
)
a_						:     int	     =		(((5_1_5, 2_2, 1_3), 5_5_5), ((6_1, 3_5, 4_9), 1_5_0))
a_						:     Union[str, Any]	     =		[2, 4, 1, 5]
a_						:     Optional[Any]	     =		len(train_data)
a_						:     Optional[int]	     =		0.009

def     __lowercase(	UpperCAmelCase__   ,   UpperCAmelCase__="train" ):


      """simple docstring"""



      return calculate_hypothesis_value(UpperCAmelCase__   ,   UpperCAmelCase__ ) - output(
          UpperCAmelCase__   ,   UpperCAmelCase__ )

def     __lowercase(	UpperCAmelCase__ ):


      """simple docstring"""



      lowerCamelCase								=		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     __lowercase(	UpperCAmelCase__   ,   UpperCAmelCase__ ):


      """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     __lowercase(	UpperCAmelCase__   ,   UpperCAmelCase__ ):


      """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     __lowercase(	UpperCAmelCase__   ,   UpperCAmelCase__=m ):


      """simple docstring"""



      lowerCamelCase								=		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     __lowercase(	UpperCAmelCase__ ):


      """simple docstring"""



      lowerCamelCase								=		summation_of_cost_derivative(UpperCAmelCase__   ,   UpperCAmelCase__ ) / m
      return cost_derivative_value

def     __lowercase(	):


      """simple docstring"""



      global parameter_vector
      # Tune these values to set a tolerance value for predicted output
      lowerCamelCase								=		0.0_0_0_0_0_2
      lowerCamelCase								=		0
      lowerCamelCase								=		0
      while True:
            j += 1
            lowerCamelCase								=		[0, 0, 0, 0]
            for i in range(0   ,   len(UpperCAmelCase__ ) ):
                  lowerCamelCase								=		get_cost_derivative(i - 1 )
                  lowerCamelCase								=		(
                      parameter_vector[i] - LEARNING_RATE * cost_derivative
                  )
            if numpy.allclose(
                UpperCAmelCase__   ,   UpperCAmelCase__   ,   atol=UpperCAmelCase__   ,   rtol=UpperCAmelCase__   ,   ):
                  break
            lowerCamelCase								=		temp_parameter_vector
      print(("Number of iterations:", j) )

def     __lowercase(	):


      """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()








def     __lowercase(	UpperCAmelCase__ ):


      """simple docstring"""



      lowerCamelCase								=		[]
      lowerCamelCase								=		[]
      lowerCamelCase								=		{
          "^": 3,
          "*": 2,
          "/": 2,
          "%": 2,
          "+": 1,
          "-": 1,
      }  # Priority of each operator
      lowerCamelCase								=		len(UpperCAmelCase__ ) if (len(UpperCAmelCase__ ) > 7) else 7

      # Print table header for output
      print(
          "Symbol".center(8 )   ,   "Stack".center(UpperCAmelCase__ )   ,   "Postfix".center(UpperCAmelCase__ )   ,   sep=" | "   ,   )
      print("-" * (print_width * 3 + 7) )

      for x in infix:
            if x.isalpha() or x.isdigit():
                  post_fix.append(UpperCAmelCase__ )  # if x is Alphabet / Digit, add it to Postfix
            elif x == "(":
                  stack.append(UpperCAmelCase__ )  # if x is "(" push to Stack
            elif x == ")":  # if x is ")" pop stack until "(" is encountered
                  while stack[-1] != "(":
                        post_fix.append(stack.pop() )  # Pop stack & add the content to Postfix
                  stack.pop()
            else:
                  if len(UpperCAmelCase__ ) == 0:
                        stack.append(UpperCAmelCase__ )  # If stack is empty, push x to stack
                  else:  # while priority of x is not > priority of element in the stack
                        while len(UpperCAmelCase__ ) > 0 and priority[x] <= priority[stack[-1]]:
                              post_fix.append(stack.pop() )  # pop stack & add to Postfix
                        stack.append(UpperCAmelCase__ )  # push x to stack

            print(
                x.center(8 )   ,   ("".join(UpperCAmelCase__ )).ljust(UpperCAmelCase__ )   ,   ("".join(UpperCAmelCase__ )).ljust(UpperCAmelCase__ )   ,   sep=" | "   ,   )  # Output in tabular format

      while len(UpperCAmelCase__ ) > 0:  # while stack is not empty
            post_fix.append(stack.pop() )  # pop stack & add to Postfix
            print(
                " ".center(8 )   ,   ("".join(UpperCAmelCase__ )).ljust(UpperCAmelCase__ )   ,   ("".join(UpperCAmelCase__ )).ljust(UpperCAmelCase__ )   ,   sep=" | "   ,   )  # Output in tabular format

      return "".join(UpperCAmelCase__ )  # return Postfix as str

def     __lowercase(	UpperCAmelCase__ ):


      """simple docstring"""



      lowerCamelCase								=		list(infix[::-1] )  # reverse the infix equation

      for i in range(len(UpperCAmelCase__ ) ):
            if infix[i] == "(":
                  lowerCamelCase								=		")"  # change "(" to ")"
            elif infix[i] == ")":
                  lowerCamelCase								=		"("  # change ")" to "("

      return (infix_2_postfix("".join(UpperCAmelCase__ ) ))[
          ::-1
      ]  # call infix_2_postfix on Infix, return reverse of Postfix


if __name__ == "__main__":
     a_						:     str	     =		input('\nEnter an Infix Equation = ')  # Input an Infix equation
     a_						:     List[Any]	     =		''.join(Infix.split())  # Remove spaces from the input
     print('\n\t', Infix, '(Infix) -> ', infix_2_prefix(Infix), '(Prefix)')