




import numpy

# List of input, output pairs
UpperCAmelCase_									=	(
    ((5, 2, 3), 15),
    ((6, 5, 9), 25),
    ((11, 12, 13), 41),
    ((1, 1, 1), 8),
    ((11, 12, 13), 41),
)
UpperCAmelCase_									=	(((515, 22, 13), 555), ((61, 35, 49), 150))
UpperCAmelCase_									=	[2, 4, 1, 5]
UpperCAmelCase_									=	len(train_data)
UpperCAmelCase_									=	0.009




def 					lowerCamelCase__       (						A__       :					Dict  ,			A__       :					Optional[int]="train"	):





       '''simple docstring'''



       return calculate_hypothesis_value(A__  ,			A__	) - output(
           A__  ,			A__	)




def 					lowerCamelCase__       (						A__       :					List[Any]	):





       '''simple docstring'''



       __lowerCamelCase   =						0
       for i in range(len(A__	) - 1	):
              hyp_val += data_input_tuple[i] * parameter_vector[i + 1]
       hyp_val += parameter_vector[0]
       return hyp_val




def 					lowerCamelCase__       (						A__       :					Union[str, Any]  ,			A__       :					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 					lowerCamelCase__       (						A__       :					Dict  ,			A__       :					int	):





       '''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__       (						A__       :					str  ,			A__       :					List[Any]=m	):





       '''simple docstring'''



       __lowerCamelCase   =						0
       for i in range(A__	):
              if index == -1:
                     summation_value += _error(A__	)
              else:
                     summation_value += _error(A__	) * train_data[i][0][index]
       return summation_value




def 					lowerCamelCase__       (						A__       :					str	):





       '''simple docstring'''



       __lowerCamelCase   =						summation_of_cost_derivative(A__  ,			A__	) / m
       return cost_derivative_value




def 					lowerCamelCase__       (						):





       '''simple docstring'''



       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(A__	)	):
                     __lowerCamelCase   =						get_cost_derivative(i - 1	)
                     __lowerCamelCase   =						(
                         parameter_vector[i] - LEARNING_RATE * cost_derivative
                     )
              if numpy.allclose(
                  A__  ,			A__  ,			atol=A__  ,			rtol=A__  ,			):
                     break
              __lowerCamelCase   =						temp_parameter_vector
       print(("""Number of iterations:""", j)	)




def 					lowerCamelCase__       (						):





       '''simple docstring'''



       for i in range(len(A__	)	):
              print(("""Actual output value:""", output(A__  ,			"""test"""	))	)
              print(("""Hypothesis output:""", calculate_hypothesis_value(A__  ,			"""test"""	))	)


if __name__ == "__main__":
       run_gradient_descent()
       print('\nTesting gradient descent for a linear hypothesis function.\n')
       test_gradient_descent()


from __future__ import annotations

from math import pi, sqrt




def       _snake_case	(   lowerCAmelCase							:   float   , lowerCAmelCase							:   float	):
		"""simple docstring"""







		if inductance <= 0:
				raise ValueError("Inductance cannot be 0 or negative"	)

		elif capacitance <= 0:
				raise ValueError("Capacitance cannot be 0 or negative"	)

		else:
				return (
				    "Resonant frequency",
				    float(1 / (2 * pi * (sqrt(inductance * capacitance	)))	),
				)


if __name__ == "__main__":
		import doctest

		doctest.testmod()
