
import itertools
from dataclasses import dataclass
from typing import Optional

import pyarrow as pa

import datasets
from datasets.table import table_cast


lowercase__							:							int													=     datasets.utils.logging.get_logger(__name__)






@dataclass
class     SCREAMING_SNAKE_CASE__      (							datasets.BuilderConfig      ):

							"""simple docstring"""






							_snake_case       						=					None






class     SCREAMING_SNAKE_CASE__      (							datasets.ArrowBasedBuilder      ):

							"""simple docstring"""






							_snake_case       						=					ArrowConfig



							def       A__						(					self     )->				Optional[Any]:





													'''simple docstring'''






													return datasets.DatasetInfo(features=self.config.features     )



							def       A__						(					self       ,		SCREAMING_SNAKE_CASE_     )->				int:





													'''simple docstring'''






													if not self.config.data_files:
																			raise ValueError(F"At least one data file must be specified, but got data_files={self.config.data_files}"     )
													__UpperCamelCase       					=     dl_manager.download_and_extract(self.config.data_files     )
													if isinstance(SCREAMING_SNAKE_CASE_       ,		(str, list, tuple)     ):
																			__UpperCamelCase       					=     data_files
																			if isinstance(SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_     ):
																									__UpperCamelCase       					=     [files]
																			# Use `dl_manager.iter_files` to skip hidden files in an extracted archive
																			__UpperCamelCase       					=     [dl_manager.iter_files(SCREAMING_SNAKE_CASE_     ) for file in files]
																			return [datasets.SplitGenerator(name=datasets.Split.TRAIN       ,		gen_kwargs={'''files''': files}     )]
													__UpperCamelCase       					=     []
													for split_name, files in data_files.items():
																			if isinstance(SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_     ):
																									__UpperCamelCase       					=     [files]
																			# Use `dl_manager.iter_files` to skip hidden files in an extracted archive
																			__UpperCamelCase       					=     [dl_manager.iter_files(SCREAMING_SNAKE_CASE_     ) for file in files]
																			# Infer features is they are stoed in the arrow schema
																			if self.info.features is None:
																									for file in itertools.chain.from_iterable(SCREAMING_SNAKE_CASE_     ):
																															with open(SCREAMING_SNAKE_CASE_       ,		'''rb'''     ) as f:
																																					__UpperCamelCase       					=     datasets.Features.from_arrow_schema(pa.ipc.open_stream(SCREAMING_SNAKE_CASE_     ).schema     )
																															break
																			splits.append(datasets.SplitGenerator(name=SCREAMING_SNAKE_CASE_       ,		gen_kwargs={'''files''': files}     )     )
													return splits



							def       A__						(					self       ,		SCREAMING_SNAKE_CASE_     )->				pa.Table:





													'''simple docstring'''






													if self.info.features is not None:
																			# more expensive cast to support nested features with keys in a different order
																			# allows str <-> int/float or str to Audio for example
																			__UpperCamelCase       					=     table_cast(SCREAMING_SNAKE_CASE_       ,		self.info.features.arrow_schema     )
													return pa_table



							def       A__						(					self       ,		SCREAMING_SNAKE_CASE_     )->				Union[str, Any]:





													'''simple docstring'''






													for file_idx, file in enumerate(itertools.chain.from_iterable(SCREAMING_SNAKE_CASE_     )     ):
																			with open(SCREAMING_SNAKE_CASE_       ,		'''rb'''     ) as f:
																									try:
																															for batch_idx, record_batch in enumerate(pa.ipc.open_stream(SCREAMING_SNAKE_CASE_     )     ):
																																					__UpperCamelCase       					=     pa.Table.from_batches([record_batch]     )
																																					# Uncomment for debugging (will print the Arrow table size and elements)
																																					# logger.warning(f"pa_table: {pa_table} num rows: {pa_table.num_rows}")
																																					# logger.warning('\n'.join(str(pa_table.slice(i, 1).to_pydict()) for i in range(pa_table.num_rows)))
																																					yield F"{file_idx}_{batch_idx}", self._cast_table(SCREAMING_SNAKE_CASE_     )
																									except ValueError as e:
																															logger.error(F"Failed to read file '{file}' with error {type(SCREAMING_SNAKE_CASE_     )}: {e}"     )
																															raise






from typing import Any

import numpy as np




def 		A_	(							snake_case							:				np.ndarray	) ->      bool:



						'''simple docstring'''

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

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

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

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




def 		A_	(							snake_case							:				int	) ->      Any:



						'''simple docstring'''

						__UpperCamelCase       					=     np.random.randn(snake_case	, snake_case	)
						__UpperCamelCase       					=     np.dot(snake_case	, random_matrix.T	)
						assert _is_matrix_spd(snake_case	)
						return spd_matrix




def 		A_	(							snake_case							:				np.ndarray	, snake_case							:				np.ndarray	, snake_case							:				int = 1000	, snake_case							:				float = 1e-8	, ) ->      Any:



						'''simple docstring'''

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

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

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

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

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

												# The main algorithm.

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

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

												# Update variables.
												__UpperCamelCase       					=     np.copy(snake_case	)
												__UpperCamelCase       					=     np.copy(snake_case	)
												__UpperCamelCase       					=     np.copy(snake_case	)

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

						return x




def 		A_	(							) ->      None:



						'''simple docstring'''

						__UpperCamelCase       					=     3
						__UpperCamelCase       					=     _create_spd_matrix(snake_case	)
						__UpperCamelCase       					=     np.random.randn(snake_case	, 1	)
						__UpperCamelCase       					=     np.dot(snake_case	, snake_case	)

						# Numpy solution.
						__UpperCamelCase       					=     np.linalg.solve(snake_case	, snake_case	)

						# Our implementation.
						__UpperCamelCase       					=     conjugate_gradient(snake_case	, snake_case	)

						# 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()




