


from __future__ import annotations

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

def 			_a  (				SCREAMING_SNAKE_CASE	:				NDArray[floataa]    , SCREAMING_SNAKE_CASE	:				NDArray[floataa]    , SCREAMING_SNAKE_CASE	:				list[int]    , SCREAMING_SNAKE_CASE	:				int    , ):







 """simple docstring"""



 UpperCamelCase__       ,				UpperCamelCase__					:    Any          =   coefficient_matrix.shape
 UpperCamelCase__       ,				UpperCamelCase__					:    Dict          =   constant_matrix.shape

 if rowsa != colsa:
  UpperCamelCase__					:    List[str]          =   F"Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}"
  raise ValueError(SCREAMING_SNAKE_CASE     )

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

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

 if len(SCREAMING_SNAKE_CASE     ) != rowsa:
  UpperCamelCase__					:    Optional[Any]          =   (
      '''Number of initial values must be equal to number of rows in coefficient '''
      F"matrix but received {len(SCREAMING_SNAKE_CASE     )} and {rowsa}"
  )
  raise ValueError(SCREAMING_SNAKE_CASE     )

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

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

 UpperCamelCase__       ,				UpperCamelCase__					:    Union[str, Any]          =   table.shape

 strictly_diagonally_dominant(SCREAMING_SNAKE_CASE     )

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

 return [float(SCREAMING_SNAKE_CASE     ) for i in new_val]

def 			_a  (				SCREAMING_SNAKE_CASE	:				NDArray[floataa]     ):







 """simple docstring"""



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

 UpperCamelCase__					:    Any          =   True

 for i in range(0    , SCREAMING_SNAKE_CASE     ):
  UpperCamelCase__					:    Dict          =   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 TYPE_CHECKING

from ..utils import _LazyModule


__UpperCamelCase       :       int						       =				{
    "config": [
        "EXTERNAL_DATA_FORMAT_SIZE_LIMIT",
        "OnnxConfig",
        "OnnxConfigWithPast",
        "OnnxSeq2SeqConfigWithPast",
        "PatchingSpec",
    ],
    "convert": ["export", "validate_model_outputs"],
    "features": ["FeaturesManager"],
    "utils": ["ParameterFormat", "compute_serialized_parameters_size"],
}


if TYPE_CHECKING:
       from .config import (
           EXTERNAL_DATA_FORMAT_SIZE_LIMIT,
           OnnxConfig,
           OnnxConfigWithPast,
           OnnxSeqaSeqConfigWithPast,
           PatchingSpec,
       )
       from .convert import export, validate_model_outputs
       from .features import FeaturesManager
       from .utils import ParameterFormat, compute_serialized_parameters_size

else:
       import sys

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


