




from typing import Any

import numpy as np






def    snake_case   (				A     )				->				bool:




	'''simple docstring'''


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

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

	# Get eigenvalues and eignevectors for a symmetric matrix.
	lowerCamelCase_  ,     lowerCamelCase_				:						Tuple				  =				np.linalg.eigh(A     )

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






def    snake_case   (				A     )				->				Any:




	'''simple docstring'''


	lowerCamelCase_				:						Optional[int]				  =				np.random.randn(A		,  A     )
	lowerCamelCase_				:						List[Any]				  =				np.dot(A		,  random_matrix.T     )
	assert _is_matrix_spd(A     )
	return spd_matrix






def    snake_case   (				A		,  A		,  A = 1000		,  A = 1e-8		,  )				->				Any:




	'''simple docstring'''


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

	# Initialize solution guess, residual, search direction.
	lowerCamelCase_				:						List[str]				  =				np.zeros((np.shape(A     )[0], 1)     )
	lowerCamelCase_				:						int				  =				np.copy(A     )
	lowerCamelCase_				:						Optional[int]				  =				np.copy(A     )

	# Set initial errors in solution guess and residual.
	lowerCamelCase_				:						Dict				  =				1e9
	lowerCamelCase_				:						int				  =				1e9
	lowerCamelCase_				:						Dict				  =				1e9

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

	while error > tol:
		# Save this value so we only calculate the matrix-vector product once.
		lowerCamelCase_				:						List[Any]				  =				np.dot(A		,  A     )

		# The main algorithm.

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

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

		# Update variables.
		lowerCamelCase_				:						Union[str, Any]				  =				np.copy(A     )
		lowerCamelCase_				:						Any				  =				np.copy(A     )
		lowerCamelCase_				:						int				  =				np.copy(A     )

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

	return x






def    snake_case   (				)				->				None:




	'''simple docstring'''


	lowerCamelCase_				:						int				  =				3
	lowerCamelCase_				:						List[str]				  =				_create_spd_matrix(A     )
	lowerCamelCase_				:						List[str]				  =				np.random.randn(A		,  1     )
	lowerCamelCase_				:						str				  =				np.dot(A		,  A     )

	# Numpy solution.
	lowerCamelCase_				:						Dict				  =				np.linalg.solve(A		,  A     )

	# Our implementation.
	lowerCamelCase_				:						Tuple				  =				conjugate_gradient(A		,  A     )

	# 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()






"""simple docstring"""
import platform
from argparse import ArgumentParser

import huggingface_hub
import pandas
import pyarrow

from datasets import __version__ as version
from datasets.commands import BaseDatasetsCLICommand






def 				__lowerCAmelCase					(					__lowerCAmelCase			:		Union[str, Any]						)    ->       int:
 return EnvironmentCommand()







class  _SCREAMING_SNAKE_CASE       (     SCREAMING_SNAKE_CASE__				):



 '''simple docstring'''





 @staticmethod
 def lowercase_      (lowerCAmelCase__   ):

  '''simple docstring'''







  _UpperCamelCase      :	Optional[Any]					      =  parser.add_parser("env"					,     help="Print relevant system environment info."   )
  download_parser.set_defaults(func=lowerCAmelCase__   )






 def lowercase_      (self   ):

  '''simple docstring'''







  _UpperCamelCase      :	Any					      =  {
      "`datasets` version": version,
      "Platform": platform.platform(),
      "Python version": platform.python_version(),
      "Huggingface_hub version": huggingface_hub.__version__,
      "PyArrow version": pyarrow.__version__,
      "Pandas version": pandas.__version__,
  }

  print("\nCopy-and-paste the text below in your GitHub issue.\n"   )
  print(self.format_dict(lowerCAmelCase__   )   )

  return info






 @staticmethod
 def lowercase_      (lowerCAmelCase__   ):

  '''simple docstring'''







  return "\n".join([F"- {prop}: {val}" for prop, val in d.items()]   ) + "\n"



