



import posixpath
from pathlib import Path
from unittest.mock import patch

import pytest
from fsspec.implementations.local import AbstractFileSystem, LocalFileSystem, stringify_path
from fsspec.registry import _registry as _fsspec_registry
class lowerCAmelCase_       (   A_			):







	'''simple docstring'''




	A_       :     Union[str, Any]									=		'mock'

	def __init__(	self   ,       *lowerCamelCase   ,       lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				super().__init__()
				a__					=  LocalFileSystem(*lowerCamelCase   ,       **lowerCamelCase       )
				a__					=  Path(lowerCamelCase       ).resolve().as_posix() + """/"""

	def 				_A			(	self   ,       lowerCamelCase   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				a__					=  posixpath.join(self.local_root_dir   ,       self._strip_protocol(lowerCamelCase       )       )
				return self._fs.mkdir(lowerCamelCase   ,       *lowerCamelCase   ,       **lowerCamelCase       )

	def 				_A			(	self   ,       lowerCamelCase   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				a__					=  posixpath.join(self.local_root_dir   ,       self._strip_protocol(lowerCamelCase       )       )
				return self._fs.makedirs(lowerCamelCase   ,       *lowerCamelCase   ,       **lowerCamelCase       )

	def 				_A			(	self   ,       lowerCamelCase       ):



				'''simple docstring'''


				a__					=  posixpath.join(self.local_root_dir   ,       self._strip_protocol(lowerCamelCase       )       )
				return self._fs.rmdir(lowerCamelCase       )

	def 				_A			(	self   ,       lowerCamelCase   ,       lowerCamelCase=True   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				a__					=  posixpath.join(self.local_root_dir   ,       self._strip_protocol(lowerCamelCase       )       )
				a__					=  self._fs.ls(lowerCamelCase   ,       detail=lowerCamelCase   ,       *lowerCamelCase   ,       **lowerCamelCase       )
				if detail:
							return [{**info, "name": info["name"][len(self.local_root_dir       ) :]} for info in out]
				else:
							return [name[len(self.local_root_dir       ) :] for name in out]

	def 				_A			(	self   ,       lowerCamelCase   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				a__					=  posixpath.join(self.local_root_dir   ,       self._strip_protocol(lowerCamelCase       )       )
				a__					=  dict(self._fs.info(lowerCamelCase   ,       *lowerCamelCase   ,       **lowerCamelCase       )       )
				a__					=  out["""name"""][len(self.local_root_dir       ) :]
				return out

	def 				_A			(	self   ,       lowerCamelCase   ,       lowerCamelCase   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				a__					=  posixpath.join(self.local_root_dir   ,       self._strip_protocol(lowerCamelCase       )       )
				a__					=  posixpath.join(self.local_root_dir   ,       self._strip_protocol(lowerCamelCase       )       )
				return self._fs.cp_file(lowerCamelCase   ,       lowerCamelCase   ,       *lowerCamelCase   ,       **lowerCamelCase       )

	def 				_A			(	self   ,       lowerCamelCase   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				a__					=  posixpath.join(self.local_root_dir   ,       self._strip_protocol(lowerCamelCase       )       )
				return self._fs.rm_file(lowerCamelCase   ,       *lowerCamelCase   ,       **lowerCamelCase       )

	def 				_A			(	self   ,       lowerCamelCase   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				a__					=  posixpath.join(self.local_root_dir   ,       self._strip_protocol(lowerCamelCase       )       )
				return self._fs.rm(lowerCamelCase   ,       *lowerCamelCase   ,       **lowerCamelCase       )

	def 				_A			(	self   ,       lowerCamelCase   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				a__					=  posixpath.join(self.local_root_dir   ,       self._strip_protocol(lowerCamelCase       )       )
				return self._fs._open(lowerCamelCase   ,       *lowerCamelCase   ,       **lowerCamelCase       )

	def 				_A			(	self   ,       lowerCamelCase       ):



				'''simple docstring'''


				a__					=  posixpath.join(self.local_root_dir   ,       self._strip_protocol(lowerCamelCase       )       )
				return self._fs.created(lowerCamelCase       )

	def 				_A			(	self   ,       lowerCamelCase       ):



				'''simple docstring'''


				a__					=  posixpath.join(self.local_root_dir   ,       self._strip_protocol(lowerCamelCase       )       )
				return self._fs.modified(lowerCamelCase       )







	@classmethod
	def 				_A			(	cls   ,       lowerCamelCase       ):



				'''simple docstring'''


				a__					=  stringify_path(lowerCamelCase       )
				if path.startswith("""mock://"""       ):
							a__					=  path[7:]
				return path


class lowerCAmelCase_       (   A_			):







	'''simple docstring'''




	A_       :     int									=		'tmp'
	A_       :     Optional[int]									=		None

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				assert self.tmp_dir is not None, "TmpDirFileSystem.tmp_dir is not set"
				super().__init__(*lowerCamelCase   ,       **lowerCamelCase   ,       local_root_dir=self.tmp_dir   ,       auto_mkdir=lowerCamelCase       )







	@classmethod
	def 				_A			(	cls   ,       lowerCamelCase       ):



				'''simple docstring'''


				a__					=  stringify_path(lowerCamelCase       )
				if path.startswith("""tmp://"""       ):
							a__					=  path[6:]
				return path




@pytest.fixture
def    UpperCAmelCase					(  ):



			'''simple docstring'''





			a__					=  MockFileSystem
			a__					=  TmpDirFileSystem
			yield
			del _fsspec_registry["mock"]
			del _fsspec_registry["tmp"]




@pytest.fixture
def    UpperCAmelCase					(  lowercase__						:					int				,					lowercase__						:					Optional[int]	):



			'''simple docstring'''





			a__					=  tmp_path_factory.mktemp("""mockfs"""	)
			return MockFileSystem(local_root_dir=lowercase__				,					auto_mkdir=lowercase__	)





@pytest.fixture
def    UpperCAmelCase					(  lowercase__						:					Any				,					lowercase__						:					List[Any]	):



			'''simple docstring'''





			a__					=  tmp_path_factory.mktemp("""tmpfs"""	)
			with patch.object(lowercase__				,					"""tmp_dir"""				,					lowercase__	):
						yield TmpDirFileSystem()






from typing import Any

import numpy as np




def    UpperCAmelCase					(  lowercase__						:					np.ndarray	):



			'''simple docstring'''





			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.
			a__				,       a__					=  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    UpperCAmelCase					(  lowercase__						:					int	):



			'''simple docstring'''





			a__					=  np.random.randn(lowercase__				,					lowercase__	)
			a__					=  np.dot(lowercase__				,					random_matrix.T	)
			assert _is_matrix_spd(lowercase__	)
			return spd_matrix




def    UpperCAmelCase					(  lowercase__						:					np.ndarray				,					lowercase__						:					np.ndarray				,					lowercase__						:					int = 1000				,					lowercase__						:					float = 1e-8				,					):



			'''simple docstring'''





			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.
			a__					=  np.zeros((np.shape(lowercase__	)[0], 1)	)
			a__					=  np.copy(lowercase__	)
			a__					=  np.copy(lowercase__	)

			# Set initial errors in solution guess and residual.
			a__					=  1e9
			a__					=  1e9
			a__					=  1e9

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

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

						# The main algorithm.

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

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

						# Update variables.
						a__					=  np.copy(lowercase__	)
						a__					=  np.copy(lowercase__	)
						a__					=  np.copy(lowercase__	)

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

			return x




def    UpperCAmelCase					(  ):



			'''simple docstring'''





			a__					=  3
			a__					=  _create_spd_matrix(lowercase__	)
			a__					=  np.random.randn(lowercase__				,					1	)
			a__					=  np.dot(lowercase__				,					lowercase__	)

			# Numpy solution.
			a__					=  np.linalg.solve(lowercase__				,					lowercase__	)

			# Our implementation.
			a__					=  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()

