



from math import pow, sqrt





def 		a__      (		*_UpperCamelCase      :			float				):
   __lowerCamelCase    				=     len(_UpperCamelCase				) > 0 and all(value > 0.0 for value in values				)
   return result





def 		a__      (		_UpperCamelCase      :			float			,_UpperCamelCase      :			float				):
   return (
       round(sqrt(molar_mass_a / molar_mass_a				)			,6				)
       if validate(_UpperCamelCase			,_UpperCamelCase				)
       else ValueError('''Input Error: Molar mass values must greater than 0.'''				)
   )





def 		a__      (		_UpperCamelCase      :			float			,_UpperCamelCase      :			float			,_UpperCamelCase      :			float				):
   return (
       round(effusion_rate * sqrt(molar_mass_a / molar_mass_a				)			,6				)
       if validate(_UpperCamelCase			,_UpperCamelCase			,_UpperCamelCase				)
       else ValueError(
           '''Input Error: Molar mass and effusion rate values must greater than 0.'''				)
   )





def 		a__      (		_UpperCamelCase      :			float			,_UpperCamelCase      :			float			,_UpperCamelCase      :			float				):
   return (
       round(effusion_rate / sqrt(molar_mass_a / molar_mass_a				)			,6				)
       if validate(_UpperCamelCase			,_UpperCamelCase			,_UpperCamelCase				)
       else ValueError(
           '''Input Error: Molar mass and effusion rate values must greater than 0.'''				)
   )





def 		a__      (		_UpperCamelCase      :			float			,_UpperCamelCase      :			float			,_UpperCamelCase      :			float				):
   return (
       round(molar_mass / pow(effusion_rate_a / effusion_rate_a			,2				)			,6				)
       if validate(_UpperCamelCase			,_UpperCamelCase			,_UpperCamelCase				)
       else ValueError(
           '''Input Error: Molar mass and effusion rate values must greater than 0.'''				)
   )





def 		a__      (		_UpperCamelCase      :			float			,_UpperCamelCase      :			float			,_UpperCamelCase      :			float				):
   return (
       round(pow(effusion_rate_a / effusion_rate_a			,2				) / molar_mass			,6				)
       if validate(_UpperCamelCase			,_UpperCamelCase			,_UpperCamelCase				)
       else ValueError(
           '''Input Error: Molar mass and effusion rate values must greater than 0.'''				)
   )











import numpy

# List of input, output pairs
a_								=       (
    ((5, 2, 3), 15),
    ((6, 5, 9), 25),
    ((11, 12, 13), 41),
    ((1, 1, 1), 8),
    ((11, 12, 13), 41),
)
a_								=       (((515, 22, 13), 555), ((61, 35, 49), 150))
a_								=       [2, 4, 1, 5]
a_								=       len(train_data)
a_								=       0.0_09





def 		a__      (		_UpperCamelCase      :			str			,_UpperCamelCase      :			List[Any]="train"				):
   return calculate_hypothesis_value(_UpperCamelCase			,_UpperCamelCase				) - output(
       _UpperCamelCase			,_UpperCamelCase				)





def 		a__      (		_UpperCamelCase      :			Optional[Any]				):
   __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 		a__      (		_UpperCamelCase      :			Tuple			,_UpperCamelCase      :			List[Any]				):
   if data_set == "train":
      return train_data[example_no][1]
   elif data_set == "test":
      return test_data[example_no][1]
   return None





def 		a__      (		_UpperCamelCase      :			List[Any]			,_UpperCamelCase      :			Union[str, Any]				):
   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__      (		_UpperCamelCase      :			Dict			,_UpperCamelCase      :			Dict=m				):
   __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 		a__      (		_UpperCamelCase      :			Optional[int]				):
   __lowerCamelCase    				=     summation_of_cost_derivative(_UpperCamelCase			,_UpperCamelCase				) / m
   return cost_derivative_value





def 		a__      (		):
   global parameter_vector
   # Tune these values to set a tolerance value for predicted output
   __lowerCamelCase    				=     0.000_002
   __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 		a__      (		):
   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()






