


import os

from apache_beam.io.filesystems import FileSystems
from apache_beam.pipeline import Pipeline

from .logging import get_logger


a					:				List[str]       =      2 << 20  # 2mb
a					:				List[Any]       =      get_logger(__name__)

class   lowerCamelCase						(	SCREAMING_SNAKE_CASE  ):

       def 					UpperCAmelCase					(      self       ):






        '''simple docstring'''






        snake_case :			List[str]							=   self._options.get_all_options().get('''runner'''       )
        return runner in [None, "DirectRunner", "PortableRunner"]







def  _UpperCAmelCase						( __lowerCamelCase			,  __lowerCamelCase			,  __lowerCamelCase=False							)		->Dict:


 '''simple docstring'''
 snake_case :			Dict							=   FileSystems
 if fs.exists(__lowerCamelCase							):
  if force_upload:
   logger.info(f'''Remote path already exist: {remote_file_path}. Overwriting it as force_upload=True.'''							)
  else:
   logger.info(f'''Remote path already exist: {remote_file_path}. Skipping it as force_upload=False.'''							)
   return
 with fs.create(__lowerCamelCase							) as remote_file:
  with open(__lowerCamelCase			,  '''rb'''							) as local_file:
   snake_case :			List[str]							=   local_file.read(__lowerCamelCase							)
   while chunk:
    remote_file.write(__lowerCamelCase							)
    snake_case :			Any							=   local_file.read(__lowerCamelCase							)






def  _UpperCAmelCase						( __lowerCamelCase			,  __lowerCamelCase			,  __lowerCamelCase=False							)		->Tuple:


 '''simple docstring'''
 snake_case :			Tuple							=   FileSystems
 if os.path.exists(__lowerCamelCase							):
  if force_download:
   logger.info(f'''Local path already exist: {remote_file_path}. Overwriting it as force_upload=True.'''							)
  else:
   logger.info(f'''Local path already exist: {remote_file_path}. Skipping it as force_upload=False.'''							)
   return
 with fs.open(__lowerCamelCase							) as remote_file:
  with open(__lowerCamelCase			,  '''wb'''							) as local_file:
   snake_case :			Any							=   remote_file.read(__lowerCamelCase							)
   while chunk:
    local_file.write(__lowerCamelCase							)
    snake_case :			Any							=   remote_file.read(__lowerCamelCase							)










from typing import Any

import numpy as np






def  _UpperCAmelCase						( __lowerCamelCase							)		->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 :			int							=   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							)		->Any:


 '''simple docstring'''
 snake_case :			Dict							=   np.random.randn(__lowerCamelCase			,  __lowerCamelCase							)
 snake_case :			List[Any]							=   np.dot(__lowerCamelCase			,  random_matrix.T							)
 assert _is_matrix_spd(__lowerCamelCase							)
 return spd_matrix






def  _UpperCAmelCase						( __lowerCamelCase			,  __lowerCamelCase			,  __lowerCamelCase = 1000			,  __lowerCamelCase = 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 :			Any							=   np.zeros((np.shape(__lowerCamelCase							)[0], 1)							)
 snake_case :			Optional[int]							=   np.copy(__lowerCamelCase							)
 snake_case :			Optional[Any]							=   np.copy(__lowerCamelCase							)

 # Set initial errors in solution guess and residual.
 snake_case :			Optional[Any]							=   1E9
 snake_case :			List[Any]							=   1E9
 snake_case :			List[str]							=   1E9

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

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

  # The main algorithm.

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

  # Calculate errors.
  snake_case :			List[Any]							=   np.linalg.norm(r - ra							)
  snake_case :			Any							=   np.linalg.norm(x - xa							)
  snake_case :			str							=   np.maximum(__lowerCamelCase			,  __lowerCamelCase							)

  # Update variables.
  snake_case :			Tuple							=   np.copy(__lowerCamelCase							)
  snake_case :			Tuple							=   np.copy(__lowerCamelCase							)
  snake_case :			List[str]							=   np.copy(__lowerCamelCase							)

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

 return x






def  _UpperCAmelCase						( )		->None:


 '''simple docstring'''
 snake_case :			str							=   3
 snake_case :			Dict							=   _create_spd_matrix(__lowerCamelCase							)
 snake_case :			str							=   np.random.randn(__lowerCamelCase			,  1							)
 snake_case :			str							=   np.dot(__lowerCamelCase			,  __lowerCamelCase							)

 # Numpy solution.
 snake_case :			Any							=   np.linalg.solve(__lowerCamelCase			,  __lowerCamelCase							)

 # Our implementation.
 snake_case :			List[str]							=   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()






