





def     _lowerCAmelCase		(  _lowerCAmelCase  ,_lowerCAmelCase = " "     ):
   '''simple docstring'''


   A_     :				str			      =	[]

   A_     :				str			      =	0
   for index, char in enumerate(_lowerCAmelCase     ):
      if char == separator:
         split_words.append(string[last_index:index]     )
         A_     :				List[Any]			      =	index + 1
      elif index + 1 == len(_lowerCAmelCase     ):
         split_words.append(string[last_index : index + 1]     )
   return split_words


if __name__ == "__main__":
      from doctest import testmod

      testmod()










from __future__ import annotations

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



def     _lowerCAmelCase		(  _lowerCAmelCase  ,_lowerCAmelCase  ,_lowerCAmelCase  ,_lowerCAmelCase  ,):
   '''simple docstring'''


   A_      ,				A_     :				int			      =	coefficient_matrix.shape
   A_      ,				A_     :				Tuple			      =	constant_matrix.shape

   if rowsa != colsa:
      A_     :				int			      =	f"""Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}"""
      raise ValueError(_lowerCAmelCase     )

   if colsa != 1:
      A_     :				List[Any]			      =	f"""Constant matrix must be nx1 but received {rowsa}x{colsa}"""
      raise ValueError(_lowerCAmelCase     )

   if rowsa != rowsa:
      A_     :				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:
      A_     :				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"""     )

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

   A_      ,				A_     :				str			      =	table.shape

   strictly_diagonally_dominant(_lowerCAmelCase     )

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

   return [float(_lowerCAmelCase     ) for i in new_val]



def     _lowerCAmelCase		(  _lowerCAmelCase     ):
   '''simple docstring'''


   A_      ,				A_     :				str			      =	table.shape

   A_     :				Any			      =	True

   for i in range(0  ,_lowerCAmelCase     ):
      A_     :				Optional[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()






