





'''simple docstring'''




from __future__ import annotations

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







def _lowerCAmelCase     (      _lowerCAmelCase       ,    _lowerCAmelCase       ,    _lowerCAmelCase       ,    _lowerCAmelCase       ,    )->     list[float]:
 __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(_lowerCAmelCase    )

 if colsa != 1:
  __UpperCAmelCase					=   F'Constant matrix must be nx1 but received {rowsa}x{colsa}'
  raise ValueError(_lowerCAmelCase    )

 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(_lowerCAmelCase    )

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

 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(_lowerCAmelCase    )

 # Iterates the whole matrix for given number of times
 for _ in range(_lowerCAmelCase    ):
  __UpperCAmelCase					=   []
  for row in range(_lowerCAmelCase    ):
   __UpperCAmelCase					=   0
   for col in range(_lowerCAmelCase    ):
    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(_lowerCAmelCase    )
  __UpperCAmelCase					=   new_val

 return [float(_lowerCAmelCase    ) for i in new_val]







def _lowerCAmelCase     (      _lowerCAmelCase    )->     bool:
 __UpperCAmelCase					,    __UpperCAmelCase					=   table.shape

 __UpperCAmelCase					=   True

 for i in range(0       ,    _lowerCAmelCase    ):
  __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()












'''simple docstring'''




from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


_A:					List[str]							=				{
    """configuration_luke""": ["""LUKE_PRETRAINED_CONFIG_ARCHIVE_MAP""", """LukeConfig"""],
    """tokenization_luke""": ["""LukeTokenizer"""],
}

try:
    if not is_torch_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    _A:					Union[str, Any]							=				[
        """LUKE_PRETRAINED_MODEL_ARCHIVE_LIST""",
        """LukeForEntityClassification""",
        """LukeForEntityPairClassification""",
        """LukeForEntitySpanClassification""",
        """LukeForMultipleChoice""",
        """LukeForQuestionAnswering""",
        """LukeForSequenceClassification""",
        """LukeForTokenClassification""",
        """LukeForMaskedLM""",
        """LukeModel""",
        """LukePreTrainedModel""",
    ]


if TYPE_CHECKING:
    from .configuration_luke import LUKE_PRETRAINED_CONFIG_ARCHIVE_MAP, LukeConfig
    from .tokenization_luke import LukeTokenizer

    try:
        if not is_torch_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_luke import (
            LUKE_PRETRAINED_MODEL_ARCHIVE_LIST,
            LukeForEntityClassification,
            LukeForEntityPairClassification,
            LukeForEntitySpanClassification,
            LukeForMaskedLM,
            LukeForMultipleChoice,
            LukeForQuestionAnswering,
            LukeForSequenceClassification,
            LukeForTokenClassification,
            LukeModel,
            LukePreTrainedModel,
        )

else:
    import sys

    _A:					str							=				_LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)





