



'''simple docstring'''




import numpy

# List of input, output pairs
a     :    Optional[int]      						=					(
    ((5, 2, 3), 1_5),
    ((6, 5, 9), 2_5),
    ((1_1, 1_2, 1_3), 4_1),
    ((1, 1, 1), 8),
    ((1_1, 1_2, 1_3), 4_1),
)
a     :    Optional[int]      						=					(((5_1_5, 2_2, 1_3), 5_5_5), ((6_1, 3_5, 4_9), 1_5_0))
a     :    Dict      						=					[2, 4, 1, 5]
a     :    Tuple      						=					len(train_data)
a     :    Optional[int]      						=					0.0_0_9



def    __lowerCamelCase						(      _lowercase			,       _lowercase="train"	)   ->    List[Any]:
							return calculate_hypothesis_value(__A			,       __A	) - output(
							    __A			,       __A	)



def    __lowerCamelCase						(      _lowercase	)   ->    Dict:
							UpperCAmelCase  :	str							  =	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						(      _lowercase			,       _lowercase	)   ->    Any:
							if data_set == "train":
														return train_data[example_no][1]
							elif data_set == "test":
														return test_data[example_no][1]
							return None



def    __lowerCamelCase						(      _lowercase			,       _lowercase	)   ->    str:
							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						(      _lowercase			,       _lowercase=m	)   ->    str:
							UpperCAmelCase  :	List[Any]							  =	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						(      _lowercase	)   ->    Tuple:
							UpperCAmelCase  :	List[Any]							  =	summation_of_cost_derivative(__A			,       __A	) / m
							return cost_derivative_value



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



def    __lowerCamelCase						(      )   ->    List[str]:
							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()






'''simple docstring'''




def    __lowerCamelCase						(      _lowercase = "The quick brown fox jumps over the lazy dog"			,       )   ->    bool:
							UpperCAmelCase  :	Union[str, Any]							  =	set()

							# Replace all the whitespace in our sentence
							UpperCAmelCase  :	List[str]							  =	input_str.replace(""" """			,       """"""	)
							for alpha in input_str:
														if "a" <= alpha.lower() <= "z":
																					frequency.add(alpha.lower()	)
							return len(_lowercase	) == 2_6



def    __lowerCamelCase						(      _lowercase = "The quick brown fox jumps over the lazy dog"			,       )   ->    bool:
							UpperCAmelCase  :	Tuple							  =	[False] * 2_6
							for char in input_str:
														if char.islower():
																					UpperCAmelCase  :	Any							  =	True
														elif char.isupper():
																					UpperCAmelCase  :	Union[str, Any]							  =	True
							return all(_lowercase	)



def    __lowerCamelCase						(      _lowercase = "The quick brown fox jumps over the lazy dog"			,       )   ->    bool:
							return len({char for char in input_str.lower() if char.isalpha()}	) == 2_6



def    __lowerCamelCase						(      )   ->    None:
							from timeit import timeit

							UpperCAmelCase  :	str							  =	"""from __main__ import is_pangram, is_pangram_faster, is_pangram_fastest"""
							print(timeit("""is_pangram()"""			,       setup=_lowercase	)	)
							print(timeit("""is_pangram_faster()"""			,       setup=_lowercase	)	)
							print(timeit("""is_pangram_fastest()"""			,       setup=_lowercase	)	)
							# 5.348480500048026, 2.6477354579837993, 1.8470395830227062
							# 5.036091582966037, 2.644472333951853,  1.8869528750656173


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							benchmark()

