




'''simple docstring'''






from __future__ import annotations

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






def 		UpperCamelCase__      (		__SCREAMING_SNAKE_CASE				,      __SCREAMING_SNAKE_CASE				,      __SCREAMING_SNAKE_CASE				,      __SCREAMING_SNAKE_CASE				,      )    ->   list[float]:
      snake_case__      ,							snake_case__       :   List[Any]	      =    coefficient_matrix.shape
      snake_case__      ,							snake_case__       :   Dict	      =    constant_matrix.shape

      if rowsa != colsa:
            snake_case__       :   Optional[Any]	      =    f"Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}"
            raise ValueError(__SCREAMING_SNAKE_CASE		)

      if colsa != 1:
            snake_case__       :   str	      =    f"Constant matrix must be nx1 but received {rowsa}x{colsa}"
            raise ValueError(__SCREAMING_SNAKE_CASE		)

      if rowsa != rowsa:
            snake_case__       :   Optional[int]	      =    (
                '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:
            snake_case__       :   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'		)

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

      snake_case__      ,							snake_case__       :   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		):
            snake_case__       :   List[Any]	      =    []
            for row in range(__SCREAMING_SNAKE_CASE		):
                  snake_case__       :   Optional[int]	      =    0
                  for col in range(__SCREAMING_SNAKE_CASE		):
                        if col == row:
                              snake_case__       :   Tuple	      =    table[row][col]
                        elif col == cols - 1:
                              snake_case__       :   Union[str, Any]	      =    table[row][col]
                        else:
                              temp += (-1) * table[row][col] * init_val[col]
                  snake_case__       :   List[str]	      =    (temp + val) / denom
                  new_val.append(__SCREAMING_SNAKE_CASE		)
            snake_case__       :   str	      =    new_val

      return [float(__SCREAMING_SNAKE_CASE		) for i in new_val]






def 		UpperCamelCase__      (		__SCREAMING_SNAKE_CASE		)    ->   bool:
      snake_case__      ,							snake_case__       :   Any	      =    table.shape

      snake_case__       :   int	      =    True

      for i in range(0				,      __SCREAMING_SNAKE_CASE		):
            snake_case__       :   str	      =    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()






'''simple docstring'''






# flake8: noqa
# Lint as: python3
A_			      =		[
    "VerificationMode",
    "Version",
    "disable_progress_bar",
    "enable_progress_bar",
    "is_progress_bar_enabled",
    "experimental",
]

from .info_utils import VerificationMode
from .logging import disable_progress_bar, enable_progress_bar, is_progress_bar_enabled
from .version import Version
from .experimental import experimental
