

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__												=						0.009



def   __UpperCAmelCase					(      __a :     List[str]						,__a :     Optional[int]="train"      )     ->	str:

					"""simple docstring"""

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



def   __UpperCAmelCase					(      __a :     Dict      )     ->	Optional[Any]:

					"""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   __UpperCAmelCase					(      __a :     Optional[int]						,__a :     List[Any]      )     ->	Optional[int]:

					"""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   __UpperCAmelCase					(      __a :     Tuple						,__a :     Tuple      )     ->	List[str]:

					"""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   __UpperCAmelCase					(      __a :     Any						,__a :     Optional[Any]=m      )     ->	List[Any]:

					"""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   __UpperCAmelCase					(      __a :     Tuple      )     ->	Optional[int]:

					"""simple docstring"""

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



def   __UpperCAmelCase					(      )     ->	Any:

					"""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   __UpperCAmelCase					(      )     ->	Any:

					"""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()





'''simple docstring'''




from random import randint, random







def 						lowerCAmelCase_							(  snake_case__						,							snake_case__						,							snake_case__						,							snake_case__ = False						,							snake_case__ = False						,							snake_case__ = 5						,							):




    '''simple docstring'''



    A			:  List[str]   =		[[-1] * number_of_cells]  # Create a highway without any car
    A			:  Optional[Any]   =		0
    A			:  Tuple   =		max(snake_case__						,							0		)
    while i < number_of_cells:
        A			:  Optional[int]   =		(
            randint(0						,							snake_case__		) if random_speed else initial_speed
        )  # Place the cars
        i += (
            randint(1						,							max_speed * 2		) if random_frequency else frequency
        )  # Arbitrary number, may need tuning
    return highway







def 						lowerCAmelCase_							(  snake_case__						,							snake_case__		):




    '''simple docstring'''



    A			:  Dict   =		0
    A			:  str   =		highway_now[car_index + 1 :]
    for cell in range(len(snake_case__		)		):  # May need a better name for this
        if cells[cell] != -1:  # If the cell is not empty then
            return distance  # we have the distance we wanted
        distance += 1
    # Here if the car is near the end of the highway
    return distance + get_distance(snake_case__						,							-1		)







def 						lowerCAmelCase_							(  snake_case__						,							snake_case__						,							snake_case__		):




    '''simple docstring'''



    A			:  int   =		len(snake_case__		)
    # Beforce calculations, the highway is empty
    A			:  int   =		[-1] * number_of_cells

    for car_index in range(snake_case__		):
        if highway_now[car_index] != -1:
            # Add 1 to the current speed of the car and cap the speed
            A			:  Optional[Any]   =		min(highway_now[car_index] + 1						,							snake_case__		)
            # Number of empty cell before the next car
            A			:  List[str]   =		get_distance(snake_case__						,							snake_case__		) - 1
            # We can't have the car causing an accident
            A			:  Union[str, Any]   =		min(next_highway[car_index]						,							snake_case__		)
            if random() < probability:
                # Randomly, a driver will slow down
                A			:  List[str]   =		max(next_highway[car_index] - 1						,							0		)
    return next_highway







def 						lowerCAmelCase_							(  snake_case__						,							snake_case__						,							snake_case__						,							snake_case__		):




    '''simple docstring'''



    A			:  Optional[Any]   =		len(highway[0]		)

    for i in range(snake_case__		):
        A			:  int   =		update(highway[i]						,							snake_case__						,							snake_case__		)
        A			:  Any   =		[-1] * number_of_cells

        for car_index in range(snake_case__		):
            A			:  Dict   =		next_speeds_calculated[car_index]
            if speed != -1:
                # Change the position based on the speed (with % to create the loop)
                A			:  Dict   =		(car_index + speed) % number_of_cells
                # Commit the change of position
                A			:  List[str]   =		speed
        highway.append(snake_case__		)

    return highway


if __name__ == "__main__":
      import doctest

      doctest.testmod()




