from typing import Any

import numpy as np


def SCREAMING_SNAKE_CASE					(  lowercase_:						np.ndarray					):
       assert np.shape(lowercase_					)[0] == np.shape(lowercase_					)[1]

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

       # Get eigenvalues and eignevectors for a symmetric matrix.
       _UpperCamelCase    ,   _UpperCamelCase  :							List[str]	    =	np.linalg.eigh(lowercase_					)

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


def SCREAMING_SNAKE_CASE					(  lowercase_:						int					):
       _UpperCamelCase  :							Dict	    =	np.random.randn(lowercase_		,    lowercase_					)
       _UpperCamelCase  :							Any	    =	np.dot(lowercase_		,    random_matrix.T					)
       assert _is_matrix_spd(lowercase_					)
       return spd_matrix


def SCREAMING_SNAKE_CASE					(  lowercase_:						np.ndarray		,    lowercase_:						np.ndarray		,    lowercase_:						int = 1000		,    lowercase_:						float = 1e-8		,    ):
       assert np.shape(lowercase_					)[0] == np.shape(lowercase_					)[1]
       assert np.shape(lowercase_					)[0] == np.shape(lowercase_					)[0]
       assert _is_matrix_spd(lowercase_					)

       # Initialize solution guess, residual, search direction.
       _UpperCamelCase  :							Dict	    =	np.zeros((np.shape(lowercase_					)[0], 1)					)
       _UpperCamelCase  :							Optional[Any]	    =	np.copy(lowercase_					)
       _UpperCamelCase  :							Optional[Any]	    =	np.copy(lowercase_					)

       # Set initial errors in solution guess and residual.
       _UpperCamelCase  :							Tuple	    =	1e9
       _UpperCamelCase  :							Optional[int]	    =	1e9
       _UpperCamelCase  :							List[str]	    =	1e9

       # Set iteration counter to threshold number of iterations.
       _UpperCamelCase  :							List[str]	    =	0

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

              # The main algorithm.

              # Update search direction magnitude.
              _UpperCamelCase  :							str	    =	np.dot(ra.T		,    lowercase_					) / np.dot(pa.T		,    lowercase_					)
              # Update solution guess.
              _UpperCamelCase  :							List[str]	    =	xa + alpha * pa
              # Calculate new residual.
              _UpperCamelCase  :							Union[str, Any]	    =	ra - alpha * w
              # Calculate new Krylov subspace scale.
              _UpperCamelCase  :							Union[str, Any]	    =	np.dot(r.T		,    lowercase_					) / np.dot(ra.T		,    lowercase_					)
              # Calculate new A conjuage search direction.
              _UpperCamelCase  :							int	    =	r + beta * pa

              # Calculate errors.
              _UpperCamelCase  :							int	    =	np.linalg.norm(r - ra					)
              _UpperCamelCase  :							Union[str, Any]	    =	np.linalg.norm(x - xa					)
              _UpperCamelCase  :							Dict	    =	np.maximum(lowercase_		,    lowercase_					)

              # Update variables.
              _UpperCamelCase  :							Union[str, Any]	    =	np.copy(lowercase_					)
              _UpperCamelCase  :							Any	    =	np.copy(lowercase_					)
              _UpperCamelCase  :							Optional[Any]	    =	np.copy(lowercase_					)

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

       return x


def SCREAMING_SNAKE_CASE					(  ):
       _UpperCamelCase  :							Optional[Any]	    =	3
       _UpperCamelCase  :							List[str]	    =	_create_spd_matrix(lowercase_					)
       _UpperCamelCase  :							Tuple	    =	np.random.randn(lowercase_		,    1					)
       _UpperCamelCase  :							List[Any]	    =	np.dot(lowercase_		,    lowercase_					)

       # Numpy solution.
       _UpperCamelCase  :							int	    =	np.linalg.solve(lowercase_		,    lowercase_					)

       # Our implementation.
       _UpperCamelCase  :							List[Any]	    =	conjugate_gradient(lowercase_		,    lowercase_					)

       # 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()




from __future__ import annotations

from statistics import mean


def SCREAMING_SNAKE_CASE					(  lowercase_:						list[int]					):
       _UpperCamelCase  :							str	    =	2
       _UpperCamelCase  :							Optional[int]	    =	list(lowercase_					)
       _UpperCamelCase  :							Union[str, Any]	    =	[0] * len(lowercase_					)
       _UpperCamelCase  :							List[str]	    =	0
       while True:
              _UpperCamelCase  :							List[str]	    =	True
              for i, burst_time in enumerate(lowercase_					):
                     if rem_burst_times[i] > 0:
                            _UpperCamelCase  :							List[str]	    =	False
                            if rem_burst_times[i] > quantum:
                                   t += quantum
                                   rem_burst_times[i] -= quantum
                            else:
                                   t += rem_burst_times[i]
                                   _UpperCamelCase  :							str	    =	t - burst_time
                                   _UpperCamelCase  :							Union[str, Any]	    =	0
              if done is True:
                     return waiting_times


def SCREAMING_SNAKE_CASE					(  lowercase_:						list[int]		,    lowercase_:						list[int]					):
       return [burst + waiting for burst, waiting in zip(lowercase_		,    lowercase_					)]


if __name__ == "__main__":
 UpperCAmelCase      		=					[3, 5, 7]
 UpperCAmelCase      		=					calculate_waiting_times(burst_times)
 UpperCAmelCase      		=					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}''')



