




'''simple docstring'''



from __future__ import annotations

from statistics import mean







def 			_UpperCamelCase (_lowerCamelCase							:     list[int]	)->   list[int]:




     '''simple docstring'''





     __snake_case    					=  2
     __snake_case    					=  list(_lowerCamelCase	)
     __snake_case    					=  [0] * len(_lowerCamelCase	)
     __snake_case    					=  0
     while True:
          __snake_case    					=  True
          for i, burst_time in enumerate(_lowerCamelCase	):
               if rem_burst_times[i] > 0:
                    __snake_case    					=  False
                    if rem_burst_times[i] > quantum:
                         t += quantum
                         rem_burst_times[i] -= quantum
                    else:
                         t += rem_burst_times[i]
                         __snake_case    					=  t - burst_time
                         __snake_case    					=  0
          if done is True:
               return waiting_times







def 			_UpperCamelCase (_lowerCamelCase							:     list[int]   ,	_lowerCamelCase							:     list[int]	)->   list[int]:




     '''simple docstring'''





     return [burst + waiting for burst, waiting in zip(_lowerCamelCase   ,	_lowerCamelCase	)]


if __name__ == "__main__":
     UpperCAmelCase_       :  List[str]      =		[3, 5, 7]
     UpperCAmelCase_       :  List[str]      =		calculate_waiting_times(burst_times)
     UpperCAmelCase_       :  str      =		calculate_turn_around_times(burst_times, waiting_times)
     print('''Process ID \tBurst Time \tWaiting Time \tTurnaround Time''')
     for i, burst_time in enumerate(burst_times):
          print(
              F"""  {i + 1}\t\t  {burst_time}\t\t  {waiting_times[i]}\t\t  """
              F"""{turn_around_times[i]}"""
          )
     print(F"""\nAverage waiting time = {mean(waiting_times):.5f}""")
     print(F"""Average turn around time = {mean(turn_around_times):.5f}""")












'''simple docstring'''



from typing import Any

import numpy as np







def 			_UpperCamelCase (_lowerCamelCase							:     np.ndarray	)->   bool:




     '''simple docstring'''





     assert np.shape(_lowerCamelCase	)[0] == np.shape(_lowerCamelCase	)[1]

     # If matrix not symmetric, exit right away.
     if np.allclose(_lowerCamelCase   ,	matrix.T	) is False:
          return False

     # Get eigenvalues and eignevectors for a symmetric matrix.
     __snake_case					,    __snake_case    					=  np.linalg.eigh(_lowerCamelCase	)

     # Check sign of all eigenvalues.
     # np.all returns a value of type np.bool_
     return bool(np.all(eigen_values > 0	)	)







def 			_UpperCamelCase (_lowerCamelCase							:     int	)->   Any:




     '''simple docstring'''





     __snake_case    					=  np.random.randn(_lowerCamelCase   ,	_lowerCamelCase	)
     __snake_case    					=  np.dot(_lowerCamelCase   ,	random_matrix.T	)
     assert _is_matrix_spd(_lowerCamelCase	)
     return spd_matrix







def 			_UpperCamelCase (_lowerCamelCase							:     np.ndarray   ,	_lowerCamelCase							:     np.ndarray   ,	_lowerCamelCase							:     int = 10_00   ,	_lowerCamelCase							:     float = 1E-8   ,	)->   Any:




     '''simple docstring'''





     assert np.shape(_lowerCamelCase	)[0] == np.shape(_lowerCamelCase	)[1]
     assert np.shape(_lowerCamelCase	)[0] == np.shape(_lowerCamelCase	)[0]
     assert _is_matrix_spd(_lowerCamelCase	)

     # Initialize solution guess, residual, search direction.
     __snake_case    					=  np.zeros((np.shape(_lowerCamelCase	)[0], 1)	)
     __snake_case    					=  np.copy(_lowerCamelCase	)
     __snake_case    					=  np.copy(_lowerCamelCase	)

     # Set initial errors in solution guess and residual.
     __snake_case    					=  1E9
     __snake_case    					=  1E9
     __snake_case    					=  1E9

     # Set iteration counter to threshold number of iterations.
     __snake_case    					=  0

     while error > tol:
          # Save this value so we only calculate the matrix-vector product once.
          __snake_case    					=  np.dot(_lowerCamelCase   ,	_lowerCamelCase	)

          # The main algorithm.

          # Update search direction magnitude.
          __snake_case    					=  np.dot(ra.T   ,	_lowerCamelCase	) / np.dot(pa.T   ,	_lowerCamelCase	)
          # Update solution guess.
          __snake_case    					=  xa + alpha * pa
          # Calculate new residual.
          __snake_case    					=  ra - alpha * w
          # Calculate new Krylov subspace scale.
          __snake_case    					=  np.dot(r.T   ,	_lowerCamelCase	) / np.dot(ra.T   ,	_lowerCamelCase	)
          # Calculate new A conjuage search direction.
          __snake_case    					=  r + beta * pa

          # Calculate errors.
          __snake_case    					=  np.linalg.norm(r - ra	)
          __snake_case    					=  np.linalg.norm(x - xa	)
          __snake_case    					=  np.maximum(_lowerCamelCase   ,	_lowerCamelCase	)

          # Update variables.
          __snake_case    					=  np.copy(_lowerCamelCase	)
          __snake_case    					=  np.copy(_lowerCamelCase	)
          __snake_case    					=  np.copy(_lowerCamelCase	)

          # Update number of iterations.
          iterations += 1
          if iterations > max_iterations:
               break

     return x







def 			_UpperCamelCase ()->   None:




     '''simple docstring'''





     __snake_case    					=  3
     __snake_case    					=  _create_spd_matrix(_lowerCamelCase	)
     __snake_case    					=  np.random.randn(_lowerCamelCase   ,	1	)
     __snake_case    					=  np.dot(_lowerCamelCase   ,	_lowerCamelCase	)

     # Numpy solution.
     __snake_case    					=  np.linalg.solve(_lowerCamelCase   ,	_lowerCamelCase	)

     # Our implementation.
     __snake_case    					=  conjugate_gradient(_lowerCamelCase   ,	_lowerCamelCase	)

     # Ensure both solutions are close to x_true (and therefore one another).
     assert np.linalg.norm(x_numpy - x_true	) <= 1E-6
     assert np.linalg.norm(x_conjugate_gradient - x_true	) <= 1E-6


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     test_conjugate_gradient()






