




'''simple docstring'''


from __future__ import annotations

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


def 						SCREAMING_SNAKE_CASE       (      a_	:							NDArray[floataa]				,					a_	:							NDArray[floataa]				,					a_	:							list[int]				,					a_	:							int				,					):
  __a	,       __a			=					coefficient_matrix.shape
  __a	,       __a			=					constant_matrix.shape

  if rowsa != colsa:
    __a			=					f"Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}"
    raise ValueError(a_			)

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

  if rowsa != rowsa:
    __a			=					(
        '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:
    __a			=					(
        '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'			)

  __a			=					np.concatenate(
      (coefficient_matrix, constant_matrix)				,					axis=1			)

  __a	,       __a			=					table.shape

  strictly_diagonally_dominant(a_			)

  # Iterates the whole matrix for given number of times
  for _ in range(a_			):
    __a			=					[]
    for row in range(a_			):
      __a			=					0
      for col in range(a_			):
        if col == row:
          __a			=					table[row][col]
        elif col == cols - 1:
          __a			=					table[row][col]
        else:
          temp += (-1) * table[row][col] * init_val[col]
      __a			=					(temp + val) / denom
      new_val.append(a_			)
    __a			=					new_val

  return [float(a_			) for i in new_val]


def 						SCREAMING_SNAKE_CASE       (      a_	:							NDArray[floataa]			):
  __a	,       __a			=					table.shape

  __a			=					True

  for i in range(0				,					a_			):
    __a			=					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'''


def 						SCREAMING_SNAKE_CASE       (      a_	:							int			):
  __a			=					0
  while num > 0:
    digit_sum += num % 10
    num //= 10
  return digit_sum


def 						SCREAMING_SNAKE_CASE       (      a_	:							int = 100			):
  __a			=					1
  __a			=					2

  for i in range(2				,					max_n + 1			):
    __a			=					pre_numerator
    __a			=					2 * i // 3 if i % 3 == 0 else 1
    __a			=					cur_numerator
    __a			=					e_cont * pre_numerator + temp

  return sum_digits(a_			)


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



