




from __future__ import annotations

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


def    A						(__A   :    NDArray[floataa]   ,				__A   :    NDArray[floataa]   ,				__A   :    list[int]   ,				__A   :    int   ,				)   ->      list[float]:







     """simple docstring"""


     UpperCAmelCase_     ,       UpperCAmelCase_          =							coefficient_matrix.shape
     UpperCAmelCase_     ,       UpperCAmelCase_          =							constant_matrix.shape

     if rowsa != colsa:
          UpperCAmelCase_          =							F"""Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}"""
          raise ValueError(__A       )

     if colsa != 1:
          UpperCAmelCase_          =							F"""Constant matrix must be nx1 but received {rowsa}x{colsa}"""
          raise ValueError(__A       )

     if rowsa != rowsa:
          UpperCAmelCase_          =							(
              '''Coefficient and constant matrices dimensions must be nxn and nx1 but '''
              F"""received {rowsa}x{colsa} and {rowsa}x{colsa}"""
          )
          raise ValueError(__A       )

     if len(__A       ) != rowsa:
          UpperCAmelCase_          =							(
              '''Number of initial values must be equal to number of rows in coefficient '''
              F"""matrix but received {len(__A       )} and {rowsa}"""
          )
          raise ValueError(__A       )

     if iterations <= 0:
          raise ValueError('''Iterations must be at least 1'''       )

     UpperCAmelCase_          =							np.concatenate(
         (coefficient_matrix, constant_matrix)   ,				axis=1       )

     UpperCAmelCase_     ,       UpperCAmelCase_          =							table.shape

     strictly_diagonally_dominant(__A       )

     # Iterates the whole matrix for given number of times
     for _ in range(__A       ):
          UpperCAmelCase_          =							[]
          for row in range(__A       ):
               UpperCAmelCase_          =							0
               for col in range(__A       ):
                    if col == row:
                         UpperCAmelCase_          =							table[row][col]
                    elif col == cols - 1:
                         UpperCAmelCase_          =							table[row][col]
                    else:
                         temp += (-1) * table[row][col] * init_val[col]
               UpperCAmelCase_          =							(temp + val) / denom
               new_val.append(__A       )
          UpperCAmelCase_          =							new_val

     return [float(__A       ) for i in new_val]


def    A						(__A   :    NDArray[floataa]       )   ->      bool:







     """simple docstring"""


     UpperCAmelCase_     ,       UpperCAmelCase_          =							table.shape

     UpperCAmelCase_          =							True

     for i in range(0   ,				__A       ):
          UpperCAmelCase_          =							0
          for j in range(0   ,				cols - 1       ):
               if i == j:
                    continue
               else:
                    total += table[i][j]

          if table[i][i] <= total:
               raise ValueError('''Coefficient matrix is not strictly diagonally dominant'''       )

     return is_diagonally_dominant


# Test Cases
if __name__ == "__main__":
    import doctest

    doctest.testmod()












from typing import List, Optional, TypeVar

from .arrow_dataset import Dataset, _concatenate_map_style_datasets, _interleave_map_style_datasets
from .dataset_dict import DatasetDict, IterableDatasetDict
from .info import DatasetInfo
from .iterable_dataset import IterableDataset, _concatenate_iterable_datasets, _interleave_iterable_datasets
from .splits import NamedSplit
from .utils import logging
from .utils.py_utils import Literal


snake_case_ : Any    		=       logging.get_logger(__name__)


snake_case_ : Optional[int]    		=       TypeVar("DatasetType", Dataset, IterableDataset)


def    A						(__A   :    List[DatasetType]   ,				__A   :    Optional[List[float]] = None   ,				__A   :    Optional[int] = None   ,				__A   :    Optional[DatasetInfo] = None   ,				__A   :    Optional[NamedSplit] = None   ,				__A   :    Literal["first_exhausted", "all_exhausted"] = "first_exhausted"   ,				)   ->      DatasetType:







     """simple docstring"""


     from .arrow_dataset import Dataset
     from .iterable_dataset import IterableDataset

     if not datasets:
          raise ValueError('''Unable to interleave an empty list of datasets.'''       )
     for i, dataset in enumerate(__A       ):
          if not isinstance(__A   ,				(Dataset, IterableDataset)       ):
               if isinstance(__A   ,				(DatasetDict, IterableDatasetDict)       ):
                    if not dataset:
                         raise ValueError(
                             F"""Expected a list of Dataset objects or a list of IterableDataset objects, but element at position {i} """
                             '''is an empty dataset dictionary.'''       )
                    raise ValueError(
                        F"""Dataset at position {i} has at least one split: {list(__A       )}\n"""
                        F"""Please pick one to interleave with the other datasets, for example: dataset['{next(iter(__A       )       )}']"""       )
               raise ValueError(
                   F"""Expected a list of Dataset objects or a list of IterableDataset objects, but element at position {i} is a {type(__A       ).__name__}."""       )
          if i == 0:
               UpperCAmelCase_     ,       UpperCAmelCase_          =							(
                   (Dataset, IterableDataset) if isinstance(__A   ,				__A       ) else (IterableDataset, Dataset)
               )
          elif not isinstance(__A   ,				__A       ):
               raise ValueError(
                   F"""Unable to interleave a {dataset_type.__name__} (at position 0) with a {other_type.__name__} (at position {i}). Expected a list of Dataset objects or a list of IterableDataset objects."""       )
     if stopping_strategy not in ["first_exhausted", "all_exhausted"]:
          raise ValueError(F"""{stopping_strategy} is not supported. Please enter a valid stopping_strategy."""       )
     if dataset_type is Dataset:
          return _interleave_map_style_datasets(
              __A   ,				__A   ,				__A   ,				info=__A   ,				split=__A   ,				stopping_strategy=__A       )
     else:
          return _interleave_iterable_datasets(
              __A   ,				__A   ,				__A   ,				info=__A   ,				split=__A   ,				stopping_strategy=__A       )


def    A						(__A   :    List[DatasetType]   ,				__A   :    Optional[DatasetInfo] = None   ,				__A   :    Optional[NamedSplit] = None   ,				__A   :    int = 0   ,				)   ->      DatasetType:







     """simple docstring"""


     if not dsets:
          raise ValueError('''Unable to concatenate an empty list of datasets.'''       )
     for i, dataset in enumerate(__A       ):
          if not isinstance(__A   ,				(Dataset, IterableDataset)       ):
               if isinstance(__A   ,				(DatasetDict, IterableDatasetDict)       ):
                    if not dataset:
                         raise ValueError(
                             F"""Expected a list of Dataset objects or a list of IterableDataset objects, but element at position {i} """
                             '''is an empty dataset dictionary.'''       )
                    raise ValueError(
                        F"""Dataset at position {i} has at least one split: {list(__A       )}\n"""
                        F"""Please pick one to interleave with the other datasets, for example: dataset['{next(iter(__A       )       )}']"""       )
               raise ValueError(
                   F"""Expected a list of Dataset objects or a list of IterableDataset objects, but element at position {i} is a {type(__A       ).__name__}."""       )
          if i == 0:
               UpperCAmelCase_     ,       UpperCAmelCase_          =							(
                   (Dataset, IterableDataset) if isinstance(__A   ,				__A       ) else (IterableDataset, Dataset)
               )
          elif not isinstance(__A   ,				__A       ):
               raise ValueError(
                   F"""Unable to interleave a {dataset_type.__name__} (at position 0) with a {other_type.__name__} (at position {i}). Expected a list of Dataset objects or a list of IterableDataset objects."""       )
     if dataset_type is Dataset:
          return _concatenate_map_style_datasets(__A   ,				info=__A   ,				split=__A   ,				axis=__A       )
     else:
          return _concatenate_iterable_datasets(__A   ,				info=__A   ,				split=__A   ,				axis=__A       )






