



"""simple docstring"""






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    (       lowercase__							,					lowercase__="train"	):
				return calculate_hypothesis_value(_UpperCAmelCase							,					_UpperCAmelCase	) - output(
				    _UpperCAmelCase							,					_UpperCAmelCase	)







def   _snake_case    (       lowercase__	):
				_lowerCamelCase  :    List[Any]					=					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   _snake_case    (       lowercase__							,					lowercase__	):
				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    (       lowercase__							,					lowercase__	):
				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    (       lowercase__							,					lowercase__=m	):
				_lowerCamelCase  :    int					=					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   _snake_case    (       lowercase__	):
				_lowerCamelCase  :    str					=					summation_of_cost_derivative(_UpperCAmelCase							,					_UpperCAmelCase	) / m
				return cost_derivative_value







def   _snake_case    (       ):
				global parameter_vector
				# Tune these values to set a tolerance value for predicted output
				_lowerCamelCase  :    Any					=					0.0_0_0_0_0_2
				_lowerCamelCase  :    Dict					=					0
				_lowerCamelCase  :    Optional[Any]					=					0
				while True:
								j += 1
								_lowerCamelCase  :    Dict					=					[0, 0, 0, 0]
								for i in range(0							,					len(_UpperCAmelCase	)	):
												_lowerCamelCase  :    Any					=					get_cost_derivative(i - 1	)
												_lowerCamelCase  :    Union[str, Any]					=					(
												    parameter_vector[i] - LEARNING_RATE * cost_derivative
												)
								if numpy.allclose(
								    _UpperCAmelCase							,					_UpperCAmelCase							,					atol=_UpperCAmelCase							,					rtol=_UpperCAmelCase							,					):
												break
								_lowerCamelCase  :    Dict					=					temp_parameter_vector
				print(('Number of iterations:', j)	)







def   _snake_case    (       ):
				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()





"""simple docstring"""






lowercase__  		=		[
    999,
    800,
    799,
    600,
    599,
    500,
    400,
    399,
    377,
    355,
    333,
    311,
    288,
    266,
    244,
    222,
    200,
    199,
    177,
    155,
    133,
    111,
    88,
    66,
    44,
    22,
    0,
]

lowercase__  		=		[
    999,
    976,
    952,
    928,
    905,
    882,
    858,
    857,
    810,
    762,
    715,
    714,
    572,
    429,
    428,
    286,
    285,
    238,
    190,
    143,
    142,
    118,
    95,
    71,
    47,
    24,
    0,
]

lowercase__  		=		[
    999,
    988,
    977,
    966,
    955,
    944,
    933,
    922,
    911,
    900,
    899,
    879,
    859,
    840,
    820,
    800,
    799,
    766,
    733,
    700,
    699,
    650,
    600,
    599,
    500,
    499,
    400,
    399,
    350,
    300,
    299,
    266,
    233,
    200,
    199,
    179,
    159,
    140,
    120,
    100,
    99,
    88,
    77,
    66,
    55,
    44,
    33,
    22,
    11,
    0,
]

lowercase__  		=		[
    999,
    995,
    992,
    989,
    985,
    981,
    978,
    975,
    971,
    967,
    964,
    961,
    957,
    956,
    951,
    947,
    942,
    937,
    933,
    928,
    923,
    919,
    914,
    913,
    908,
    903,
    897,
    892,
    887,
    881,
    876,
    871,
    870,
    864,
    858,
    852,
    846,
    840,
    834,
    828,
    827,
    820,
    813,
    806,
    799,
    792,
    785,
    784,
    777,
    770,
    763,
    756,
    749,
    742,
    741,
    733,
    724,
    716,
    707,
    699,
    698,
    688,
    677,
    666,
    656,
    655,
    645,
    634,
    623,
    613,
    612,
    598,
    584,
    570,
    569,
    555,
    541,
    527,
    526,
    505,
    484,
    483,
    462,
    440,
    439,
    396,
    395,
    352,
    351,
    308,
    307,
    264,
    263,
    220,
    219,
    176,
    132,
    88,
    44,
    0,
]

lowercase__  		=		[
    999,
    997,
    995,
    992,
    990,
    988,
    986,
    984,
    981,
    979,
    977,
    975,
    972,
    970,
    968,
    966,
    964,
    961,
    959,
    957,
    956,
    954,
    951,
    949,
    946,
    944,
    941,
    939,
    936,
    934,
    931,
    929,
    926,
    924,
    921,
    919,
    916,
    914,
    913,
    910,
    907,
    905,
    902,
    899,
    896,
    893,
    891,
    888,
    885,
    882,
    879,
    877,
    874,
    871,
    870,
    867,
    864,
    861,
    858,
    855,
    852,
    849,
    846,
    843,
    840,
    837,
    834,
    831,
    828,
    827,
    824,
    821,
    817,
    814,
    811,
    808,
    804,
    801,
    798,
    795,
    791,
    788,
    785,
    784,
    780,
    777,
    774,
    770,
    766,
    763,
    760,
    756,
    752,
    749,
    746,
    742,
    741,
    737,
    733,
    730,
    726,
    722,
    718,
    714,
    710,
    707,
    703,
    699,
    698,
    694,
    690,
    685,
    681,
    677,
    673,
    669,
    664,
    660,
    656,
    655,
    650,
    646,
    641,
    636,
    632,
    627,
    622,
    618,
    613,
    612,
    607,
    602,
    596,
    591,
    586,
    580,
    575,
    570,
    569,
    563,
    557,
    551,
    545,
    539,
    533,
    527,
    526,
    519,
    512,
    505,
    498,
    491,
    484,
    483,
    474,
    466,
    457,
    449,
    440,
    439,
    428,
    418,
    407,
    396,
    395,
    381,
    366,
    352,
    351,
    330,
    308,
    307,
    286,
    264,
    263,
    242,
    220,
    219,
    176,
    175,
    132,
    131,
    88,
    44,
    0,
]

lowercase__  		=		[
    999,
    991,
    982,
    974,
    966,
    958,
    950,
    941,
    933,
    925,
    916,
    908,
    900,
    899,
    874,
    850,
    825,
    800,
    799,
    700,
    600,
    500,
    400,
    300,
    200,
    100,
    0,
]

lowercase__  		=		[
    999,
    992,
    985,
    978,
    971,
    964,
    957,
    949,
    942,
    935,
    928,
    921,
    914,
    907,
    900,
    899,
    879,
    859,
    840,
    820,
    800,
    799,
    766,
    733,
    700,
    699,
    650,
    600,
    599,
    500,
    499,
    400,
    399,
    300,
    299,
    200,
    199,
    100,
    99,
    0,
]

lowercase__  		=		[
    999,
    996,
    992,
    989,
    985,
    982,
    979,
    975,
    972,
    968,
    965,
    961,
    958,
    955,
    951,
    948,
    944,
    941,
    938,
    934,
    931,
    927,
    924,
    920,
    917,
    914,
    910,
    907,
    903,
    900,
    899,
    891,
    884,
    876,
    869,
    861,
    853,
    846,
    838,
    830,
    823,
    815,
    808,
    800,
    799,
    788,
    777,
    766,
    755,
    744,
    733,
    722,
    711,
    700,
    699,
    688,
    677,
    666,
    655,
    644,
    633,
    622,
    611,
    600,
    599,
    585,
    571,
    557,
    542,
    528,
    514,
    500,
    499,
    485,
    471,
    457,
    442,
    428,
    414,
    400,
    399,
    379,
    359,
    340,
    320,
    300,
    299,
    279,
    259,
    240,
    220,
    200,
    199,
    166,
    133,
    100,
    99,
    66,
    33,
    0,
]