





'''simple docstring'''
from __future__ import annotations

import numpy as np
from numpy import floataa
from numpy.typing import NDArray
def 				lowercase__   (   __lowercase						:  NDArray[floataa]				,  __lowercase						:  NDArray[floataa]				,  __lowercase						:  list[int]				,  __lowercase						:  int				,  ) ->      List[str]:



       """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(SCREAMING_SNAKE_CASE__     )

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

       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(SCREAMING_SNAKE_CASE__     )

       if len(SCREAMING_SNAKE_CASE__     ) != rowsa:
              __UpperCamelCase       =  (
                  '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       =  np.concatenate(
           (coefficient_matrix, constant_matrix)				,  axis=1     )

       __UpperCamelCase       ,						__UpperCamelCase       =  table.shape

       strictly_diagonally_dominant(SCREAMING_SNAKE_CASE__     )

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

       return [float(SCREAMING_SNAKE_CASE__     ) for i in new_val]
def 				lowercase__   (   __lowercase						:  NDArray[floataa]     ) ->      Union[str, Any]:



       """simple docstring"""






       __UpperCamelCase       ,						__UpperCamelCase       =  table.shape

       __UpperCamelCase       =  True

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




def 						_UpperCAmelCase				(			SCREAMING_SNAKE_CASE__			:					int = 10**12				):
     __UpperCamelCase    							=1
     __UpperCamelCase    							=0

     __UpperCamelCase    							=1
     __UpperCamelCase    							=1

     while numerator <= 2 * min_total - 1:
          prev_numerator += 2 * numerator
          numerator += 2 * prev_numerator

          prev_denominator += 2 * denominator
          denominator += 2 * prev_denominator

     return (denominator + 1) // 2


if __name__ == "__main__":
   print(f"""{solution() = }""")





