




'''simple docstring'''


def 						snake_case_       (UpperCamelCase			:    list					,		UpperCamelCase			:    list					,		UpperCamelCase			:    int ):





							'''simple docstring'''


							_a      	=							len(UpperCamelCase )
							_a      	=							[[0] * n for i in range(UpperCamelCase )]
							for i in range(UpperCamelCase ):
														_a      	=							y_points[i]

							for i in range(2					,		UpperCamelCase ):
														for j in range(UpperCamelCase					,		UpperCamelCase ):
																					_a      	=							(
																					    (xa - x_points[j - i + 1]) * q[j][i - 1]
																					    - (xa - x_points[j]) * q[j - 1][i - 1]
																					) / (x_points[j] - x_points[j - i + 1])

							return [q[n - 1][n - 1], q]


if __name__ == "__main__":
				import doctest

				doctest.testmod()








a__: str							   =						'0.21.0'

from .accelerator import Accelerator
from .big_modeling import (
    cpu_offload,
    cpu_offload_with_hook,
    disk_offload,
    dispatch_model,
    init_empty_weights,
    init_on_device,
    load_checkpoint_and_dispatch,
)
from .data_loader import skip_first_batches
from .launchers import debug_launcher, notebook_launcher
from .state import PartialState
from .utils import (
    DeepSpeedPlugin,
    DistributedDataParallelKwargs,
    DistributedType,
    FullyShardedDataParallelPlugin,
    GradScalerKwargs,
    InitProcessGroupKwargs,
    find_executable_batch_size,
    infer_auto_device_map,
    is_rich_available,
    load_checkpoint_in_model,
    synchronize_rng_states,
)


if is_rich_available():
       from .utils import rich





