



import numpy

# List of input, output pairs
UpperCamelCase__ =						(
    ((5, 2, 3), 15),
    ((6, 5, 9), 25),
    ((11, 12, 13), 41),
    ((1, 1, 1), 8),
    ((11, 12, 13), 41),
)
UpperCamelCase__ =						(((5_15, 22, 13), 5_55), ((61, 35, 49), 1_50))
UpperCamelCase__ =						[2, 4, 1, 5]
UpperCamelCase__ =						len(train_data)
UpperCamelCase__ =						0.009






def  UpperCAmelCase__    (    lowercase__						,       lowercase__="train"   ) ->      Optional[int]:
						return calculate_hypothesis_value(lowercase__						,       lowercase__   ) - output(
						    lowercase__						,       lowercase__   )






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






def  UpperCAmelCase__    (    lowercase__						,       lowercase__   ) ->      Optional[int]:
						if data_set == "train":
												return train_data[example_no][1]
						elif data_set == "test":
												return test_data[example_no][1]
						return None






def  UpperCAmelCase__    (    lowercase__						,       lowercase__   ) ->      Dict:
						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__    (    lowercase__						,       lowercase__=m   ) ->      Union[str, Any]:
						__lowercase					=				0
						for i in range(lowercase__   ):
												if index == -1:
																		summation_value += _error(lowercase__   )
												else:
																		summation_value += _error(lowercase__   ) * train_data[i][0][index]
						return summation_value






def  UpperCAmelCase__    (    lowercase__   ) ->      Optional[Any]:
						__lowercase					=				summation_of_cost_derivative(lowercase__						,       lowercase__   ) / m
						return cost_derivative_value






def  UpperCAmelCase__    (    ) ->      Tuple:
						global parameter_vector
						# Tune these values to set a tolerance value for predicted output
						__lowercase					=				0.000002
						__lowercase					=				0
						__lowercase					=				0
						while True:
												j += 1
												__lowercase					=				[0, 0, 0, 0]
												for i in range(0						,       len(lowercase__   )   ):
																		__lowercase					=				get_cost_derivative(i - 1   )
																		__lowercase					=				(
																		    parameter_vector[i] - LEARNING_RATE * cost_derivative
																		)
												if numpy.allclose(
												    lowercase__						,       lowercase__						,       atol=lowercase__						,       rtol=lowercase__						,       ):
																		break
												__lowercase					=				temp_parameter_vector
						print(("""Number of iterations:""", j)   )






def  UpperCAmelCase__    (    ) ->      Any:
						for i in range(len(lowercase__   )   ):
												print(("""Actual output value:""", output(lowercase__						,       """test"""   ))   )
												print(("""Hypothesis output:""", calculate_hypothesis_value(lowercase__						,       """test"""   ))   )


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










import unittest

import numpy as np






def  UpperCAmelCase__    (    lowercase__						,       lowercase__						,       lowercase__						,       lowercase__ = None						,       ) ->      np.ndarray:
						__lowercase					=				np.shape(lowercase__   )
						__lowercase					=				np.shape(lowercase__   )
						__lowercase					=				np.shape(lowercase__   )

						if shape_a[0] != shape_b[0]:
												__lowercase					=				(
												    """Expected the same number of rows for A and B. """
												    F"Instead found A of size {shape_a} and B of size {shape_b}"
												)
												raise ValueError(lowercase__   )

						if shape_b[1] != shape_c[1]:
												__lowercase					=				(
												    """Expected the same number of columns for B and C. """
												    F"Instead found B of size {shape_b} and C of size {shape_c}"
												)
												raise ValueError(lowercase__   )

						__lowercase					=				pseudo_inv
						if a_inv is None:
												try:
																		__lowercase					=				np.linalg.inv(lowercase__   )
												except np.linalg.LinAlgError:
																		raise ValueError(
																		    """Input matrix A is not invertible. Cannot compute Schur complement."""   )

						return mat_c - mat_b.T @ a_inv @ mat_b
class 			_lowerCAmelCase   ( unittest.TestCase			):






			"""simple docstring"""





			def 		snake_case__			(				self	:       Dict   )						->					None:
									"""simple docstring"""







									__lowercase					=				np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]   )
									__lowercase					=				np.array([[0, 3], [3, 0], [2, 3]]   )
									__lowercase					=				np.array([[2, 1], [6, 3]]   )

									__lowercase					=				schur_complement(lowercase			,     lowercase			,     lowercase   )

									__lowercase					=				np.block([[a, b], [b.T, c]]   )

									__lowercase					=				np.linalg.det(lowercase   )
									__lowercase					=				np.linalg.det(lowercase   )
									__lowercase					=				np.linalg.det(lowercase   )

									self.assertAlmostEqual(lowercase			,     det_a * det_s   )





			def 		snake_case__			(				self	:       Tuple   )						->					None:
									"""simple docstring"""







									__lowercase					=				np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]   )
									__lowercase					=				np.array([[0, 3], [3, 0], [2, 3]]   )
									__lowercase					=				np.array([[2, 1], [6, 3]]   )

									with self.assertRaises(lowercase   ):
															schur_complement(lowercase			,     lowercase			,     lowercase   )







			def 		snake_case__			(				self	:       Tuple   )						->					None:
									"""simple docstring"""







									__lowercase					=				np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]   )
									__lowercase					=				np.array([[0, 3], [3, 0], [2, 3]]   )
									__lowercase					=				np.array([[2, 1, 3], [6, 3, 5]]   )

									with self.assertRaises(lowercase   ):
															schur_complement(lowercase			,     lowercase			,     lowercase   )


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			unittest.main()





