


"""simple docstring"""






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



def 			A__		(					_UpperCAmelCase    :      NDArray[floataa]				,    _UpperCAmelCase    :      NDArray[floataa]	)							->	NDArray[floataa]:

	'''simple docstring'''


	snake_case__,					snake_case__  :						Any		=      np.shape(_UpperCAmelCase	)

	snake_case__  :						NDArray[floataa]		=      np.zeros((rows, 1)				,    dtype=_UpperCAmelCase	)
	for row in reversed(range(_UpperCAmelCase	)	):
		snake_case__  :						Dict		=      0
		for col in range(row + 1				,    _UpperCAmelCase	):
			total += coefficients[row, col] * x[col]

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

	return x



def 			A__		(					_UpperCAmelCase    :      NDArray[floataa]				,    _UpperCAmelCase    :      NDArray[floataa]	)							->	NDArray[floataa]:

	'''simple docstring'''


	snake_case__,					snake_case__  :						str		=      np.shape(_UpperCAmelCase	)
	if rows != columns:
		return np.array(()				,    dtype=_UpperCAmelCase	)

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

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

	snake_case__  :						List[str]		=      retroactive_resolution(
	    augmented_mat[:, 0:columns]				,    augmented_mat[:, columns : columns + 1]	)

	return x


if __name__ == "__main__":
					import doctest

					doctest.testmod()







'''simple docstring'''





import os
import sys
from pathlib import Path

import pytest

from datasets import Dataset, IterableDataset
from datasets.distributed import split_dataset_by_node

from .utils import execute_subprocess_async, get_torch_dist_unique_port, require_torch
def 	snake_case_							(				):
      snake_case_    							=				Dataset.from_dict({"i": range(17      )}      )
      snake_case_    							=				len(_a      )
      snake_case_    							=				3
      snake_case_    							=				[
          split_dataset_by_node(_a			,       rank=_a			,       world_size=_a      ) for rank in range(_a      )
      ]
      assert sum(len(_a      ) for ds in datasets_per_rank      ) == full_size
      assert len({tuple(x.values()      ) for ds in datasets_per_rank for x in ds}      ) == full_size
def 	snake_case_							(				):
      def gen():
            return ({"i": i} for i in range(17      ))

      snake_case_    							=				3
      snake_case_    							=				IterableDataset.from_generator(_a      )
      snake_case_    							=				len(list(_a      )      )
      snake_case_    							=				[
          split_dataset_by_node(_a			,       rank=_a			,       world_size=_a      ) for rank in range(_a      )
      ]
      assert sum(len(list(_a      )      ) for ds in datasets_per_rank      ) == full_size
      assert len({tuple(x.values()      ) for ds in datasets_per_rank for x in ds}      ) == full_size
@pytest.mark.parametrize("shards_per_node"			,       [1, 2, 3]      )
def 	snake_case_							(				_a  :				List[Any]      ):
      def gen(_a  :				Dict      ):
            for shard in shards:
                  yield from ({"i": i, "shard": shard} for i in range(17      ))

      snake_case_    							=				3
      snake_case_    							=				shards_per_node * world_size
      snake_case_    							=				{"shards": [F'''shard_{shard_idx}.txt''' for shard_idx in range(_a      )]}
      snake_case_    							=				IterableDataset.from_generator(_a			,       gen_kwargs=_a      )
      snake_case_    							=				len(list(_a      )      )
      assert full_ds.n_shards == world_size * shards_per_node
      snake_case_    							=				[
          split_dataset_by_node(_a			,       rank=_a			,       world_size=_a      ) for rank in range(_a      )
      ]
      assert [ds.n_shards for ds in datasets_per_rank] == [shards_per_node] * world_size
      assert sum(len(list(_a      )      ) for ds in datasets_per_rank      ) == full_size
      assert len({tuple(x.values()      ) for ds in datasets_per_rank for x in ds}      ) == full_size
def 	snake_case_							(				):
      def gen():
            return ({"i": i} for i in range(17      ))

      snake_case_    							=				2
      snake_case_    							=				IterableDataset.from_generator(_a      )
      snake_case_    							=				len(list(_a      )      )

      snake_case_    							=				split_dataset_by_node(_a			,       rank=0			,       world_size=_a      ).shuffle(seed=42      )
      assert len(list(_a      )      ) == 1 + full_size // world_size
      with pytest.raises(_a      ):
            split_dataset_by_node(_a			,       rank=0			,       world_size=_a      ).shuffle()

      snake_case_    							=				split_dataset_by_node(full_ds.shuffle(seed=42      )			,       rank=0			,       world_size=_a      )
      assert len(list(_a      )      ) == 1 + full_size // world_size
      with pytest.raises(_a      ):
            split_dataset_by_node(full_ds.shuffle()			,       rank=0			,       world_size=_a      )
@pytest.mark.parametrize("streaming"			,       [False, True]      )
@require_torch
@pytest.mark.skipif(os.name == "nt"			,       reason="execute_subprocess_async doesn't support windows"      )
@pytest.mark.integration
def 	snake_case_							(				_a  :				Any      ):
      snake_case_    							=				2
      snake_case_    							=				get_torch_dist_unique_port()
      snake_case_    							=				Path(_a      ).resolve().parent / "distributed_scripts" / "launch_torch_distributed.py"
      snake_case_    							=				F'''
        -m torch.distributed.launch
        --nproc_per_node={nproc_per_node}
        --master_port={master_port}
        {test_script}
    '''.split()
      snake_case_    							=				F'''
        --streaming={streaming}
    '''.split()
      snake_case_    							=				[sys.executable] + distributed_args + args
      execute_subprocess_async(_a			,       env=os.environ.copy()      )




@pytest.mark.parametrize(
    "nproc_per_node, num_workers"			,       [
        (2, 2),  # each node has 2 shards and each worker has 1 shards
        (3, 2),  # each node uses all the shards but skips examples, and each worker has 2 shards
    ]			,       )
@require_torch
@pytest.mark.skipif(os.name == "nt"			,       reason="execute_subprocess_async doesn't support windows"      )
@pytest.mark.integration
def 	snake_case_							(				_a  :				int			,       _a  :				List[Any]      ):
      snake_case_    							=				True
      snake_case_    							=				get_torch_dist_unique_port()
      snake_case_    							=				Path(_a      ).resolve().parent / "distributed_scripts" / "launch_torch_distributed.py"
      snake_case_    							=				F'''
        -m torch.distributed.launch
        --nproc_per_node={nproc_per_node}
        --master_port={master_port}
        {test_script}
    '''.split()
      snake_case_    							=				F'''
        --streaming={streaming}
        --num_workers={num_workers}
    '''.split()
      snake_case_    							=				[sys.executable] + distributed_args + args
      execute_subprocess_async(_a			,       env=os.environ.copy()      )

