


from __future__ import annotations

import numpy as np
from numpy import floataa
from numpy.typing import NDArray
def 				UpperCAmelCase_					(							__snake_case     ,						__snake_case     ,						__snake_case     ,						__snake_case     ,						)     ->			list[float]:







 """simple docstring"""


 _lowercase      ,    _lowercase							      =coefficient_matrix.shape
 _lowercase      ,    _lowercase							      =constant_matrix.shape

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

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

 if rowsa != rowsa:
  _lowercase							      =(
      '''Coefficient and constant matrices dimensions must be nxn and nx1 but '''
      F"received {rowsa}x{colsa} and {rowsa}x{colsa}"
  )
  raise ValueError(__snake_case						)

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

 if iterations <= 0:
  raise ValueError('''Iterations must be at least 1'''						)

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

 _lowercase      ,    _lowercase							      =table.shape

 strictly_diagonally_dominant(__snake_case						)

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

 return [float(__snake_case						) for i in new_val]
def 				UpperCAmelCase_					(							__snake_case						)     ->			bool:







 """simple docstring"""


 _lowercase      ,    _lowercase							      =table.shape

 _lowercase							      =True

 for i in range(0     ,						__snake_case						):
  _lowercase							      =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'''




import unittest

import numpy as np
import torch

from .utils_summarization import build_mask, compute_token_type_ids, process_story, truncate_or_pad







class 	_lowerCAmelCase							(			unittest.TestCase ):


	def     _a	(self							):
				A_	:						Optional[Any]	=     10


	def     _a	(self							):
				A_	:						Dict	=     [1, 2, 3, 4]
				A_	:						List[Any]	=     [1, 2, 3, 4, 0, 0, 0, 0, 0, 0]
				self.assertEqual(truncate_or_pad(lowercase       ,      self.block_size       ,      0							)       ,      lowercase							)


	def     _a	(self							):
				A_	:						List[Any]	=     [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
				A_	:						Tuple	=     [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
				self.assertEqual(truncate_or_pad(lowercase       ,      self.block_size       ,      0							)       ,      lowercase							)


	def     _a	(self							):
				A_	:						Optional[Any]	=     [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]
				A_	:						Any	=     [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
				self.assertEqual(truncate_or_pad(lowercase       ,      self.block_size       ,      0							)       ,      lowercase							)


	def     _a	(self							):
				A_	:						List[str]	=     """It was the year of Our Lord one thousand seven hundred and
        seventy-five.\n\nSpiritual revelations were conceded to England at that
        favoured period, as at this."""
				A_,    A_	:						Dict	=     process_story(lowercase							)
				self.assertEqual(lowercase       ,      []							)


	def     _a	(self							):
				A_	:						Optional[int]	=     """"""
				A_,    A_	:						List[str]	=     process_story(lowercase							)
				self.assertEqual(lowercase       ,      []							)
				self.assertEqual(lowercase       ,      []							)


	def     _a	(self							):
				A_	:						Optional[Any]	=     (
				    """It was the year of Our Lord one thousand seven hundred and """
				    """seventy-five\n\nSpiritual revelations were conceded to England """
				    """at that favoured period, as at this.\n@highlight\n\nIt was the best of times"""
				)
				A_,    A_	:						int	=     process_story(lowercase							)

				A_	:						Optional[Any]	=     [
				    """It was the year of Our Lord one thousand seven hundred and seventy-five.""",
				    """Spiritual revelations were conceded to England at that favoured period, as at this.""",
				]
				self.assertEqual(lowercase       ,      lowercase							)

				A_	:						Dict	=     ["""It was the best of times."""]
				self.assertEqual(lowercase       ,      lowercase							)


	def     _a	(self							):
				A_	:						Optional[int]	=     torch.tensor([1, 2, 3, 4]							)
				A_	:						Dict	=     torch.tensor([1, 1, 1, 1]							)
				np.testing.assert_array_equal(build_mask(lowercase       ,      0							).numpy()       ,      expected.numpy()							)


	def     _a	(self							):
				A_	:						str	=     torch.tensor([1, 2, 3, 4, 23, 23, 23]							)
				A_	:						str	=     torch.tensor([1, 1, 1, 1, 0, 0, 0]							)
				np.testing.assert_array_equal(build_mask(lowercase       ,      23							).numpy()       ,      expected.numpy()							)


	def     _a	(self							):
				A_	:						Any	=     torch.tensor([8, 2, 3, 4, 1, 1, 1]							)
				A_	:						List[str]	=     torch.tensor([1, 1, 1, 1, 0, 0, 0]							)
				np.testing.assert_array_equal(build_mask(lowercase       ,      1							).numpy()       ,      expected.numpy()							)


	def     _a	(self							):
				A_	:						List[Any]	=     101
				A_	:						List[Any]	=     torch.tensor([[1, 2, 3, 4, 5, 6], [1, 2, 3, 101, 5, 6], [1, 101, 3, 4, 101, 6]]							)
				A_	:						List[str]	=     torch.tensor([[1, 1, 1, 1, 1, 1], [1, 1, 1, 0, 0, 0], [1, 0, 0, 0, 1, 1]]							)

				A_	:						Dict	=     compute_token_type_ids(lowercase       ,      lowercase							)
				np.testing.assert_array_equal(lowercase       ,      lowercase							)