


from __future__ import annotations

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

def    lowercase_	(	_A    :					NDArray[floataa]					,      _A    :					NDArray[floataa]					,      _A    :					list[int]					,      _A    :					int					,      ):

      """simple docstring"""




      lowerCamelCase__					,     lowerCamelCase__	:       Optional[int]					=						coefficient_matrix.shape
      lowerCamelCase__					,     lowerCamelCase__	:       Union[str, Any]					=						constant_matrix.shape

      if rowsa != colsa:
            lowerCamelCase__	:       Dict					=						F"Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}"
            raise ValueError(_A		)

      if colsa != 1:
            lowerCamelCase__	:       Optional[Any]					=						F"Constant matrix must be nx1 but received {rowsa}x{colsa}"
            raise ValueError(_A		)

      if rowsa != rowsa:
            lowerCamelCase__	:       Union[str, Any]					=						(
                "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:
            lowerCamelCase__	:       Union[str, Any]					=						(
                "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"		)

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

      lowerCamelCase__					,     lowerCamelCase__	:       Optional[Any]					=						table.shape

      strictly_diagonally_dominant(_A		)

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

      return [float(_A		) for i in new_val]

def    lowercase_	(	_A    :					NDArray[floataa]		):

      """simple docstring"""




      lowerCamelCase__					,     lowerCamelCase__	:       Optional[Any]					=						table.shape

      lowerCamelCase__	:       List[str]					=						True

      for i in range(0					,      _A		):
            lowerCamelCase__	:       Dict					=						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    lowercase_	(	_A    :					int		):

      """simple docstring"""




      if not isinstance(_A					,      _A		):
            lowerCamelCase__	:       List[str]					=						F"Input value of [number={number}] must be an integer"
            raise TypeError(_A		)
      if number < 0:
            return False
      lowerCamelCase__	:       Dict					=						number * number
      while number > 0:
            if number % 10 != number_square % 10:
                  return False
            number //= 10
            number_square //= 10
      return True


if __name__ == "__main__":
    import doctest

    doctest.testmod()


