
'''simple docstring'''




def 						lowerCAmelCase_							(  snake_case__						,							snake_case__		):




    '''simple docstring'''



    A			:  Tuple   =		len(snake_case__		)
    A			:  List[Any]   =		[[False] * (required_sum + 1) for _ in range(arr_len + 1		)]

    # for each arr value, a sum of zero(0) can be formed by not taking any element
    # hence True/1
    for i in range(arr_len + 1		):
        A			:  Dict   =		True

    # sum is not zero and set is empty then false
    for i in range(1						,							required_sum + 1		):
        A			:  Optional[Any]   =		False

    for i in range(1						,							arr_len + 1		):
        for j in range(1						,							required_sum + 1		):
            if arr[i - 1] > j:
                A			:  Optional[Any]   =		subset[i - 1][j]
            if arr[i - 1] <= j:
                A			:  Any   =		subset[i - 1][j] or subset[i - 1][j - arr[i - 1]]

    return subset[arr_len][required_sum]


if __name__ == "__main__":
      import doctest

      doctest.testmod()






'''simple docstring'''




import numpy

# List of input, output pairs
lowercase     :							Any       						=     (
    ((5, 2, 3), 15),
    ((6, 5, 9), 25),
    ((11, 12, 13), 41),
    ((1, 1, 1), 8),
    ((11, 12, 13), 41),
)
lowercase     :							str       						=     (((5_15, 22, 13), 5_55), ((61, 35, 49), 1_50))
lowercase     :							Union[str, Any]       						=     [2, 4, 1, 5]
lowercase     :							Any       						=     len(train_data)
lowercase     :							Optional[int]       						=     0.0_09







def 						lowerCAmelCase_							(  snake_case__						,							snake_case__="train"		):




    '''simple docstring'''



    return calculate_hypothesis_value(snake_case__						,							snake_case__		) - output(
        snake_case__						,							snake_case__		)







def 						lowerCAmelCase_							(  snake_case__		):




    '''simple docstring'''



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







def 						lowerCAmelCase_							(  snake_case__						,							snake_case__		):




    '''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_							(  snake_case__						,							snake_case__		):




    '''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_							(  snake_case__						,							snake_case__=m		):




    '''simple docstring'''



    A			:  List[Any]   =		0
    for i in range(snake_case__		):
        if index == -1:
            summation_value += _error(snake_case__		)
        else:
            summation_value += _error(snake_case__		) * train_data[i][0][index]
    return summation_value







def 						lowerCAmelCase_							(  snake_case__		):




    '''simple docstring'''



    A			:  List[Any]   =		summation_of_cost_derivative(snake_case__						,							snake_case__		) / m
    return cost_derivative_value







def 						lowerCAmelCase_							(  ):




    '''simple docstring'''



    global parameter_vector
    # Tune these values to set a tolerance value for predicted output
    A			:  Dict   =		0.00_00_02
    A			:  Optional[Any]   =		0
    A			:  int   =		0
    while True:
        j += 1
        A			:  List[str]   =		[0, 0, 0, 0]
        for i in range(0						,							len(snake_case__		)		):
            A			:  Union[str, Any]   =		get_cost_derivative(i - 1		)
            A			:  Tuple   =		(
                parameter_vector[i] - LEARNING_RATE * cost_derivative
            )
        if numpy.allclose(
            snake_case__						,							snake_case__						,							atol=snake_case__						,							rtol=snake_case__						,							):
            break
        A			:  List[Any]   =		temp_parameter_vector
    print(('''Number of iterations:''', j)		)







def 						lowerCAmelCase_							(  ):




    '''simple docstring'''



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


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




