




from __future__ import annotations

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


def    A						(__A   :    NDArray[floataa]   ,				__A   :    NDArray[floataa]   ,				__A   :    list[int]   ,				__A   :    int   ,				)   ->      list[float]:







     """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(__A       )

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

     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(__A       )

     if len(__A       ) != rowsa:
          UpperCAmelCase_          =							(
              '''Number of initial values must be equal to number of rows in coefficient '''
              F"""matrix but received {len(__A       )} and {rowsa}"""
          )
          raise ValueError(__A       )

     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(__A       )

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

     return [float(__A       ) for i in new_val]


def    A						(__A   :    NDArray[floataa]       )   ->      bool:







     """simple docstring"""


     UpperCAmelCase_     ,       UpperCAmelCase_          =							table.shape

     UpperCAmelCase_          =							True

     for i in range(0   ,				__A       ):
          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()








__lowerCamelCase							=       {
    "joule": 1.0,
    "kilojoule": 10_00,
    "megajoule": 1_00_00_00,
    "gigajoule": 10_00_00_00_00,
    "wattsecond": 1.0,
    "watthour": 36_00,
    "kilowatthour": 3_60_00_00,
    "newtonmeter": 1.0,
    "calorie_nutr": 41_86.8,
    "kilocalorie_nutr": 4_18_68_00.00,
    "electronvolt": 1.602_176_634e-19,
    "britishthermalunit_it": 10_55.0_55_85,
    "footpound": 1.35_5818,
}


def 			UpperCamelCase					(    __lowerCamelCase     : str				,					__lowerCamelCase     : str				,					__lowerCamelCase     : float    ):
       if to_type not in ENERGY_CONVERSION or from_type not in ENERGY_CONVERSION:
              snake_case       :   List[Any]							=      (
                  f"""Incorrect 'from_type' or 'to_type' value: {from_type!r}, {to_type!r}\n"""
                  f"""Valid values are: {', '.join(__lowerCamelCase    )}"""
              )
              raise ValueError(__lowerCamelCase    )
       return value * ENERGY_CONVERSION[from_type] / ENERGY_CONVERSION[to_type]


if __name__ == "__main__":
   import doctest

   doctest.testmod()





