






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__							  =						(((515, 22, 13), 555), ((61, 35, 49), 150))
UpperCAmelCase__							  =						[2, 4, 1, 5]
UpperCAmelCase__							  =						len(train_data)
UpperCAmelCase__							  =						0.009
def 		_a       ( a					:int      ,				a					:Optional[int]="train"					)				->     Any:
 return calculate_hypothesis_value(a      ,				a					) - output(
     a      ,				a					)
def 		_a       ( a					:Tuple					)				->     str:
 a						    = 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 		_a       ( a					:str      ,				a					:Optional[Any]					)				->     str:
 if data_set == "train":
  return train_data[example_no][1]
 elif data_set == "test":
  return test_data[example_no][1]
 return None
def 		_a       ( a					:Tuple      ,				a					:Dict					)				->     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 		_a       ( a					:Dict      ,				a					:Optional[Any]=m					)				->     Dict:
 a						    = 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 		_a       ( a					:str					)				->     Dict:
 a						    = summation_of_cost_derivative(a      ,				a					) / m
 return cost_derivative_value
def 		_a       ( )				->     Optional[Any]:
 global parameter_vector
 # Tune these values to set a tolerance value for predicted output
 a						    = 0.000_002
 a						    = 0
 a						    = 0
 while True:
  j += 1
  a						    = [0, 0, 0, 0]
  for i in range(0      ,				len(a					)					):
   a						    = get_cost_derivative(i - 1					)
   a						    = (
       parameter_vector[i] - LEARNING_RATE * cost_derivative
   )
  if numpy.allclose(
      a      ,				a      ,				atol=a      ,				rtol=a      ,				):
   break
  a						    = temp_parameter_vector
 print(('''Number of iterations:''', j)					)
def 		_a       ( )				->     Union[str, Any]:
 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()










from typing import Any

import numpy as np
def 		_a       ( a					:np.ndarray					)				->     bool:
 return np.array_equal(a      ,				matrix.conjugate().T					)
def 		_a       ( a					:np.ndarray      ,				a					:np.ndarray					)				->     Any:
 a						    = v.conjugate().T
 a						    = v_star.dot(a					)
 assert isinstance(a      ,				np.ndarray					)
 return (v_star_dot.dot(a					)) / (v_star.dot(a					))
def 		_a       ( )				->     None:
 a						    = np.array([[2, 2 + 1j, 4], [2 - 1j, 3, 1j], [4, -1j, 1]]					)
 a						    = np.array([[1], [2], [3]]					)
 assert is_hermitian(a					), F"""{a} is not hermitian."""
 print(rayleigh_quotient(a      ,				a					)					)

 a						    = np.array([[1, 2, 4], [2, 3, -1], [4, -1, 1]]					)
 assert is_hermitian(a					), F"""{a} is not hermitian."""
 assert rayleigh_quotient(a      ,				a					) == float(3					)


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     tests()


