



import numpy as np
from numpy import floataa
from numpy.typing import NDArray





def 						__lowerCamelCase       (      __magic_name__	:  NDArray[floataa]     , __magic_name__	:  NDArray[floataa]						):
							a__							,			a__:       Tuple											=np.shape(__magic_name__						)

							a__:       NDArray[floataa]											=np.zeros((rows, 1)     , dtype=__magic_name__						)
							for row in reversed(range(__magic_name__						)						):
														a__:       Union[str, Any]											=0
														for col in range(row + 1     , __magic_name__						):
																					total += coefficients[row, col] * x[col]

														a__:       str											=(vector[row] - total) / coefficients[row, row]

							return x





def 						__lowerCamelCase       (      __magic_name__	:  NDArray[floataa]     , __magic_name__	:  NDArray[floataa]						):
							a__							,			a__:       int											=np.shape(__magic_name__						)
							if rows != columns:
														return np.array(()     , dtype=__magic_name__						)

							# augmented matrix
							a__:       NDArray[floataa]											=np.concatenate((coefficients, vector)     , axis=1						)
							a__:       List[Any]											=augmented_mat.astype("float64"						)

							# scale the matrix leaving it triangular
							for row in range(rows - 1						):
														a__:       Optional[Any]											=augmented_mat[row, row]
														for col in range(row + 1     , __magic_name__						):
																					a__:       str											=augmented_mat[col, row] / pivot
																					augmented_mat[col, :] -= factor * augmented_mat[row, :]

							a__:       List[Any]											=retroactive_resolution(
							    augmented_mat[:, 0:columns]     , augmented_mat[:, columns : columns + 1]						)

							return x


if __name__ == "__main__":
		import doctest

		doctest.testmod()










import json
import os
from dataclasses import dataclass

import numpy as np
import pyarrow as pa

import datasets
from utils import get_duration


__UpperCAmelCase						  =     10_00_00_00_00_00
__UpperCAmelCase						  =     1_00_00

__UpperCAmelCase  ,							__UpperCAmelCase						  =     os.path.split(__file__)
__UpperCAmelCase						  =     os.path.join(RESULTS_BASEPATH, '''results''', RESULTS_FILENAME.replace('''.py''', '''.json'''))





def 						__lowerCamelCase       (      __magic_name__	:  int     , __magic_name__	:  int						):
							a__:       Any											=pa.Table.from_pydict({"col": [0] * chunk_size}						)
							a__:       Optional[Any]											=pa.concat_tables([table] * (num_examples // chunk_size)						)
							return datasets.Dataset(__magic_name__     , fingerprint="table_100B"						)


@dataclass
class 	lowerCamelCase__ :
						_lowerCAmelCase								= 42
						_lowerCAmelCase								= 42
						_lowerCAmelCase								= 42
						_lowerCAmelCase								= 42


						def   _lowerCamelCase			( self						:  Union[str, Any]			):
													a__:       Tuple											=np.random.default_rng(self.seed			)
													a__:       Tuple											=rng.integers(low=self.low      ,       high=self.high      ,       size=self.size			).tolist()


						def __iter__( self						:  Any			):
													return iter(self._sampled_values			)







						def __len__( self						:  Any			):
													return self.size





@get_duration
def 						__lowerCamelCase       (      __magic_name__	:  datasets.Dataset						):
							a__:       Union[str, Any]											=dataset[0]





@get_duration
def 						__lowerCamelCase       (      __magic_name__	:  datasets.Dataset						):
							a__:       Optional[Any]											=dataset[-1]





@get_duration
def 						__lowerCamelCase       (      __magic_name__	:  datasets.Dataset						):
							a__:       List[str]											=dataset[range(len(__magic_name__						) // 2     , len(__magic_name__						) // 2 + 1_024						)]





@get_duration
def 						__lowerCamelCase       (      __magic_name__	:  datasets.Dataset						):
							a__:       Optional[int]											=dataset[RandIter(0     , len(__magic_name__						)     , 1_024     , seed=42						)]





def 						__lowerCamelCase       (      ):
							a__:       Dict											={"num examples": SPEED_TEST_N_EXAMPLES}
							a__:       Union[str, Any]											=(get_first_row, get_last_row, get_batch_of_aaaa_rows, get_batch_of_aaaa_random_rows)
							print("generating dataset"						)
							a__:       Dict											=generate_100B_dataset(num_examples=__magic_name__     , chunk_size=__magic_name__						)
							print("Functions"						)
							for func in functions:
														print(func.__name__						)
														a__:       Dict											=func(__magic_name__						)

							with open(__magic_name__     , "wb"						) as f:
														f.write(json.dumps(__magic_name__						).encode("utf-8"						)						)


if __name__ == "__main__":  # useful to run the profiler
		benchmark_table_100B()





