






"""simple docstring"""


from __future__ import annotations

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




def       snake_case  (A_				:NDArray[floataa]     ,      A_				:NDArray[floataa]     ,      A_				:list[int]     ,      A_				:int     ,      ):







  '''simple docstring'''

  a,					a					:      Optional[Any]    =       coefficient_matrix.shape
  a,					a					:      Any    =       constant_matrix.shape

  if rowsa != colsa:
    a					:      Optional[int]    =       f'''Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}'''
    raise ValueError(A_				)

  if colsa != 1:
    a					:      Optional[Any]    =       f'''Constant matrix must be nx1 but received {rowsa}x{colsa}'''
    raise ValueError(A_				)

  if rowsa != rowsa:
    a					:      List[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:
    a					:      List[str]    =       (
        '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					:      NDArray[floataa]    =       np.concatenate(
      (coefficient_matrix, constant_matrix)     ,      axis=1				)

  a,					a					:      Dict    =       table.shape

  strictly_diagonally_dominant(A_				)

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

  return [float(A_				) for i in new_val]




def       snake_case  (A_				:NDArray[floataa]				):







  '''simple docstring'''

  a,					a					:      List[Any]    =       table.shape

  a					:      List[Any]    =       True

  for i in range(0     ,      A_				):
    a					:      Any    =       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"""


from __future__ import annotations

import math

import numpy as np
from numpy.linalg import norm




def       snake_case  (A_				:np.ndarray     ,      A_				:np.ndarray				):







  '''simple docstring'''

  return math.sqrt(sum(pow(a - b     ,      2				) for a, b in zip(A_     ,      A_				)				)				)




def       snake_case  (A_				:np.ndarray     ,      A_				:np.ndarray				):







  '''simple docstring'''

  if dataset.ndim != value_array.ndim:
    a					:      Optional[Any]    =       (
        'Wrong input data\'s dimensions... '
        f'''dataset : {dataset.ndim}, value_array : {value_array.ndim}'''
    )
    raise ValueError(A_				)

  try:
    if dataset.shape[1] != value_array.shape[1]:
      a					:      Optional[int]    =       (
          'Wrong input data\'s shape... '
          f'''dataset : {dataset.shape[1]}, value_array : {value_array.shape[1]}'''
      )
      raise ValueError(A_				)
  except IndexError:
    if dataset.ndim != value_array.ndim:
      raise TypeError('Wrong shape'				)

  if dataset.dtype != value_array.dtype:
    a					:      Optional[Any]    =       (
        'Input data have different datatype... '
        f'''dataset : {dataset.dtype}, value_array : {value_array.dtype}'''
    )
    raise TypeError(A_				)

  a					:      Tuple    =       []

  for value in value_array:
    a					:      List[Any]    =       euclidean(A_     ,      dataset[0]				)
    a					:      int    =       dataset[0].tolist()

    for dataset_value in dataset[1:]:
      a					:      Optional[int]    =       euclidean(A_     ,      A_				)

      if dist > temp_dist:
        a					:      List[str]    =       temp_dist
        a					:      int    =       dataset_value.tolist()

    answer.append([vector, dist]				)

  return answer




def       snake_case  (A_				:np.ndarray     ,      A_				:np.ndarray				):







  '''simple docstring'''

  return np.dot(A_     ,      A_				) / (norm(A_				) * norm(A_				))


if __name__ == "__main__":
   import doctest

   doctest.testmod()




