


from __future__ import annotations

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

def 						_UpperCAmelCase				(			SCREAMING_SNAKE_CASE__			:					NDArray[floataa]			,     SCREAMING_SNAKE_CASE__			:					NDArray[floataa]			,     SCREAMING_SNAKE_CASE__			:					list[int]			,     SCREAMING_SNAKE_CASE__			:					int			,     ):
     __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 						_UpperCAmelCase				(			SCREAMING_SNAKE_CASE__			:					NDArray[floataa]				):
     __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    A						(__A   :    list   ,				__A   :    int   ,				__A   :    int = 0   ,				__A   :    int = 0       )   ->      int:







     """simple docstring"""


     UpperCAmelCase_          =							right or len(__A       ) - 1
     if left > right:
          return -1
     elif list_data[left] == key:
          return left
     elif list_data[right] == key:
          return right
     else:
          return search(__A   ,				__A   ,				left + 1   ,				right - 1       )


if __name__ == "__main__":
    import doctest

    doctest.testmod()






