

import numpy

# List of input, output pairs
lowercase_			=  (
    ((5, 2, 3), 15),
    ((6, 5, 9), 25),
    ((11, 12, 13), 41),
    ((1, 1, 1), 8),
    ((11, 12, 13), 41),
)
lowercase_			=  (((515, 22, 13), 555), ((61, 35, 49), 150))
lowercase_			=  [2, 4, 1, 5]
lowercase_			=  len(train_data)
lowercase_			=  0.009
def 						_snake_case(   SCREAMING_SNAKE_CASE__      :     Union[str, Any]   ,      SCREAMING_SNAKE_CASE__      :     Optional[int]="train"				)							->				Dict:





    '''simple docstring'''






    return calculate_hypothesis_value(SCREAMING_SNAKE_CASE__   ,      SCREAMING_SNAKE_CASE__				) - output(
        SCREAMING_SNAKE_CASE__   ,      SCREAMING_SNAKE_CASE__				)
def 						_snake_case(   SCREAMING_SNAKE_CASE__      :     Optional[int]				)							->				Union[str, Any]:





    '''simple docstring'''






    A__   				=       0
    for i in range(len(SCREAMING_SNAKE_CASE__				) - 1				):
        hyp_val += data_input_tuple[i] * parameter_vector[i + 1]
    hyp_val += parameter_vector[0]
    return hyp_val
def 						_snake_case(   SCREAMING_SNAKE_CASE__      :     str   ,      SCREAMING_SNAKE_CASE__      :     Union[str, Any]				)							->				str:





    '''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 						_snake_case(   SCREAMING_SNAKE_CASE__      :     Dict   ,      SCREAMING_SNAKE_CASE__      :     Optional[Any]				)							->				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 						_snake_case(   SCREAMING_SNAKE_CASE__      :     Union[str, Any]   ,      SCREAMING_SNAKE_CASE__      :     str=m				)							->				Dict:





    '''simple docstring'''






    A__   				=       0
    for i in range(SCREAMING_SNAKE_CASE__				):
        if index == -1:
            summation_value += _error(SCREAMING_SNAKE_CASE__				)
        else:
            summation_value += _error(SCREAMING_SNAKE_CASE__				) * train_data[i][0][index]
    return summation_value
def 						_snake_case(   SCREAMING_SNAKE_CASE__      :     List[Any]				)							->				List[Any]:





    '''simple docstring'''






    A__   				=       summation_of_cost_derivative(SCREAMING_SNAKE_CASE__   ,      SCREAMING_SNAKE_CASE__				) / m
    return cost_derivative_value
def 						_snake_case(   )							->				List[str]:





    '''simple docstring'''






    global parameter_vector
    # Tune these values to set a tolerance value for predicted output
    A__   				=       0.00_0002
    A__   				=       0
    A__   				=       0
    while True:
        j += 1
        A__   				=       [0, 0, 0, 0]
        for i in range(0   ,      len(SCREAMING_SNAKE_CASE__				)				):
            A__   				=       get_cost_derivative(i - 1				)
            A__   				=       (
                parameter_vector[i] - LEARNING_RATE * cost_derivative
            )
        if numpy.allclose(
            SCREAMING_SNAKE_CASE__   ,      SCREAMING_SNAKE_CASE__   ,      atol=SCREAMING_SNAKE_CASE__   ,      rtol=SCREAMING_SNAKE_CASE__   ,      ):
            break
        A__   				=       temp_parameter_vector
    print(('Number of iterations:', j)				)
def 						_snake_case(   )							->				Tuple:





    '''simple docstring'''






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


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




import random
def 						_snake_case(   SCREAMING_SNAKE_CASE__      :     list   ,      SCREAMING_SNAKE_CASE__      :     str				)							->				tuple:





    '''simple docstring'''






    A__				,						A__				,						A__   				=       [], [], []
    for element in data:
        if element < pivot:
            less.append(SCREAMING_SNAKE_CASE__				)
        elif element > pivot:
            greater.append(SCREAMING_SNAKE_CASE__				)
        else:
            equal.append(SCREAMING_SNAKE_CASE__				)
    return less, equal, greater

def 						_snake_case(   SCREAMING_SNAKE_CASE__      :     list   ,      SCREAMING_SNAKE_CASE__      :     int				)							->				str:





    '''simple docstring'''






    if index >= len(SCREAMING_SNAKE_CASE__				) or index < 0:
        return None

    A__   				=       items[random.randint(0   ,      len(SCREAMING_SNAKE_CASE__				) - 1				)]
    A__   				=       0
    A__				,						A__				,						A__   				=       _partition(SCREAMING_SNAKE_CASE__   ,      SCREAMING_SNAKE_CASE__				)
    A__   				=       len(SCREAMING_SNAKE_CASE__				)
    A__   				=       len(SCREAMING_SNAKE_CASE__				)

    # index is the pivot
    if m <= index < m + count:
        return pivot
    # must be in smaller
    elif m > index:
        return quick_select(SCREAMING_SNAKE_CASE__   ,      SCREAMING_SNAKE_CASE__				)
    # must be in larger
    else:
        return quick_select(SCREAMING_SNAKE_CASE__   ,      index - (m + count)				)

