



"""simple docstring"""







from __future__ import annotations

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

def 				UpperCamelCase_    (    lowerCAmelCase__      :				NDArray[floataa]    ,   lowerCAmelCase__      :				NDArray[floataa]    ,   lowerCAmelCase__      :				list[int]    ,   lowerCAmelCase__      :				int    ,   )						->   list[float]:

  """simple docstring"""




  lowerCAmelCase_						,lowerCAmelCase_   :				int								= coefficient_matrix.shape
  lowerCAmelCase_						,lowerCAmelCase_   :				Optional[Any]								= constant_matrix.shape

  if rowsa != colsa:
    lowerCAmelCase_   :				Optional[int]								= f"Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}"
    raise ValueError(lowerCAmelCase__						)

  if colsa != 1:
    lowerCAmelCase_   :				Any								= f"Constant matrix must be nx1 but received {rowsa}x{colsa}"
    raise ValueError(lowerCAmelCase__						)

  if rowsa != rowsa:
    lowerCAmelCase_   :				List[str]								= (
        '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:
    lowerCAmelCase_   :				List[Any]								= (
        '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'						)

  lowerCAmelCase_   :				NDArray[floataa]								= np.concatenate(
      (coefficient_matrix, constant_matrix)    ,   axis=1						)

  lowerCAmelCase_						,lowerCAmelCase_   :				Tuple								= table.shape

  strictly_diagonally_dominant(lowerCAmelCase__						)

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

  return [float(lowerCAmelCase__						) for i in new_val]

def 				UpperCamelCase_    (    lowerCAmelCase__      :				NDArray[floataa]						)						->   bool:

  """simple docstring"""




  lowerCAmelCase_						,lowerCAmelCase_   :				Optional[int]								= table.shape

  lowerCAmelCase_   :				Optional[Any]								= True

  for i in range(0    ,   lowerCAmelCase__						):
    lowerCAmelCase_   :				Any								= 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_flax_available,
    is_sentencepiece_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


lowercase__		:				int          =	{"""configuration_mbart""": ["""MBART_PRETRAINED_CONFIG_ARCHIVE_MAP""", """MBartConfig""", """MBartOnnxConfig"""]}

try:
     if not is_sentencepiece_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     lowercase__		:				Optional[int]          =	["""MBartTokenizer"""]

try:
     if not is_tokenizers_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     lowercase__		:				Dict          =	["""MBartTokenizerFast"""]

try:
     if not is_torch_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     lowercase__		:				Any          =	[
         """MBART_PRETRAINED_MODEL_ARCHIVE_LIST""",
         """MBartForCausalLM""",
         """MBartForConditionalGeneration""",
         """MBartForQuestionAnswering""",
         """MBartForSequenceClassification""",
         """MBartModel""",
         """MBartPreTrainedModel""",
     ]

try:
     if not is_tf_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     lowercase__		:				Tuple          =	[
         """TFMBartForConditionalGeneration""",
         """TFMBartModel""",
         """TFMBartPreTrainedModel""",
     ]

try:
     if not is_flax_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     lowercase__		:				Tuple          =	[
         """FlaxMBartForConditionalGeneration""",
         """FlaxMBartForQuestionAnswering""",
         """FlaxMBartForSequenceClassification""",
         """FlaxMBartModel""",
         """FlaxMBartPreTrainedModel""",
     ]


if TYPE_CHECKING:
     from .configuration_mbart import MBART_PRETRAINED_CONFIG_ARCHIVE_MAP, MBartConfig, MBartOnnxConfig

     try:
          if not is_sentencepiece_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .tokenization_mbart import MBartTokenizer

     try:
          if not is_tokenizers_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .tokenization_mbart_fast import MBartTokenizerFast

     try:
          if not is_torch_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_mbart import (
              MBART_PRETRAINED_MODEL_ARCHIVE_LIST,
              MBartForCausalLM,
              MBartForConditionalGeneration,
              MBartForQuestionAnswering,
              MBartForSequenceClassification,
              MBartModel,
              MBartPreTrainedModel,
          )

     try:
          if not is_tf_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_tf_mbart import TFMBartForConditionalGeneration, TFMBartModel, TFMBartPreTrainedModel

     try:
          if not is_flax_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_flax_mbart import (
              FlaxMBartForConditionalGeneration,
              FlaxMBartForQuestionAnswering,
              FlaxMBartForSequenceClassification,
              FlaxMBartModel,
              FlaxMBartPreTrainedModel,
          )

else:
     import sys

     lowercase__		:				int          =	_LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)





