





from __future__ import annotations

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



def 		A_    (					_lowerCAmelCase							,       _lowerCAmelCase							,       _lowerCAmelCase							,       _lowerCAmelCase							,       )						->			list[float]:
 UpperCamelCase     : List[Any]	     =       coefficient_matrix.shape
 UpperCamelCase     : Optional[int]	     =       constant_matrix.shape

 if rowsa != colsa:
  UpperCamelCase     : List[Any]	     =       F"""Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}"""
  raise ValueError(_lowerCAmelCase					)

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

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

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

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

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

 UpperCamelCase     : str	     =       table.shape

 strictly_diagonally_dominant(_lowerCAmelCase					)

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

 return [float(_lowerCAmelCase					) for i in new_val]



def 		A_    (					_lowerCAmelCase					)						->			bool:
 UpperCamelCase     : Dict	     =       table.shape

 UpperCamelCase     : List[Any]	     =       True

 for i in range(0							,       _lowerCAmelCase					):
  UpperCamelCase     : Union[str, 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()







import unittest

from transformers import AlbertTokenizer, AlbertTokenizerFast
from transformers.testing_utils import get_tests_dir, require_sentencepiece, require_tokenizers, slow

from ...test_tokenization_common import TokenizerTesterMixin


__lowerCamelCase	:					Dict			  =					get_tests_dir("""fixtures/spiece.model""")



@require_sentencepiece
@require_tokenizers
class  A__       (	__snake_case	,       unittest.TestCase      ):
      _UpperCAmelCase     :int						   =       AlbertTokenizer
      _UpperCAmelCase     :int						   =       AlbertTokenizerFast
      _UpperCAmelCase     :int						   =       True
      _UpperCAmelCase     :List[str]						   =       True
      _UpperCAmelCase     :Optional[Any]						   =       True





      def 	__UpperCamelCase(			self       ):
       '''simple docstring'''




       super().setUp()

       # We have a SentencePiece fixture for testing
       UpperCamelCase     : List[str]	     =       AlbertTokenizer(A_       )
       tokenizer.save_pretrained(self.tmpdirname       )





      def 	__UpperCamelCase(			self	,							A_       ):
       '''simple docstring'''




       UpperCamelCase     : List[Any]	     =       "this is a test"
       UpperCamelCase     : List[Any]	     =       "this is a test"
       return input_text, output_text





      def 	__UpperCamelCase(			self       ):
       '''simple docstring'''




       UpperCamelCase     : Union[str, Any]	     =       "<pad>"
       UpperCamelCase     : Dict	     =       0

       self.assertEqual(self.get_tokenizer()._convert_token_to_id(A_       )	,							A_       )
       self.assertEqual(self.get_tokenizer()._convert_id_to_token(A_       )	,							A_       )





      def 	__UpperCamelCase(			self       ):
       '''simple docstring'''




       UpperCamelCase     : Dict	     =       list(self.get_tokenizer().get_vocab().keys()       )

       self.assertEqual(vocab_keys[0]	,							"<pad>"       )
       self.assertEqual(vocab_keys[1]	,							"<unk>"       )
       self.assertEqual(vocab_keys[-1]	,							"▁eloquent"       )
       self.assertEqual(len(A_       )	,							3_0000       )





      def 	__UpperCamelCase(			self       ):
       '''simple docstring'''




       self.assertEqual(self.get_tokenizer().vocab_size	,							3_0000       )





      def 	__UpperCamelCase(			self       ):
       '''simple docstring'''




       if not self.test_rust_tokenizer:
        return

       UpperCamelCase     : Any	     =       self.get_tokenizer()
       UpperCamelCase     : Optional[int]	     =       self.get_rust_tokenizer()

       UpperCamelCase     : List[Any]	     =       "I was born in 92000, and this is falsé."

       UpperCamelCase     : Optional[Any]	     =       tokenizer.tokenize(A_       )
       UpperCamelCase     : Optional[int]	     =       rust_tokenizer.tokenize(A_       )
       self.assertListEqual(A_	,							A_       )

       UpperCamelCase     : Optional[Any]	     =       tokenizer.encode(A_	,							add_special_tokens=A_       )
       UpperCamelCase     : Optional[int]	     =       rust_tokenizer.encode(A_	,							add_special_tokens=A_       )
       self.assertListEqual(A_	,							A_       )

       UpperCamelCase     : List[Any]	     =       self.get_rust_tokenizer()
       UpperCamelCase     : Union[str, Any]	     =       tokenizer.encode(A_       )
       UpperCamelCase     : Optional[int]	     =       rust_tokenizer.encode(A_       )
       self.assertListEqual(A_	,							A_       )





      def 	__UpperCamelCase(			self       ):
       '''simple docstring'''




       UpperCamelCase     : List[Any]	     =       AlbertTokenizer(A_	,							keep_accents=A_       )

       UpperCamelCase     : Optional[int]	     =       tokenizer.tokenize("This is a test"       )
       self.assertListEqual(A_	,							["▁this", "▁is", "▁a", "▁test"]       )

       self.assertListEqual(tokenizer.convert_tokens_to_ids(A_       )	,							[48, 25, 21, 1289]       )

       UpperCamelCase     : Optional[Any]	     =       tokenizer.tokenize("I was born in 92000, and this is falsé."       )
       self.assertListEqual(
           A_	,							["▁i", "▁was", "▁born", "▁in", "▁9", "2000", ",", "▁and", "▁this", "▁is", "▁fal", "s", "é", "."]       )
       UpperCamelCase     : Optional[int]	     =       tokenizer.convert_tokens_to_ids(A_       )
       self.assertListEqual(A_	,							[31, 23, 386, 19, 561, 3050, 15, 17, 48, 25, 8256, 18, 1, 9]       )

       UpperCamelCase     : List[str]	     =       tokenizer.convert_ids_to_tokens(A_       )
       self.assertListEqual(
           A_	,							["▁i", "▁was", "▁born", "▁in", "▁9", "2000", ",", "▁and", "▁this", "▁is", "▁fal", "s", "<unk>", "."]	,							)





      def 	__UpperCamelCase(			self       ):
       '''simple docstring'''




       UpperCamelCase     : Optional[int]	     =       AlbertTokenizer(A_       )

       UpperCamelCase     : Dict	     =       tokenizer.encode("sequence builders"       )
       UpperCamelCase     : Tuple	     =       tokenizer.encode("multi-sequence build"       )

       UpperCamelCase     : str	     =       tokenizer.build_inputs_with_special_tokens(A_       )
       UpperCamelCase     : int	     =       tokenizer.build_inputs_with_special_tokens(A_	,							A_       )

       assert encoded_sentence == [tokenizer.cls_token_id] + text + [tokenizer.sep_token_id]
       assert encoded_pair == [tokenizer.cls_token_id] + text + [tokenizer.sep_token_id] + text_a + [
           tokenizer.sep_token_id
       ]





      @slow
      def 	__UpperCamelCase(			self       ):
       '''simple docstring'''




       UpperCamelCase     : List[Any]	     =       {"attention_mask": [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "input_ids": [[2, 2_1970, 13, 5, 6092, 167, 28, 7103, 2153, 673, 8, 7028, 1_2051, 18, 17, 7103, 2153, 673, 8, 3515, 1_8684, 8, 4461, 6, 1927, 297, 8, 1_2060, 2607, 18, 13, 5, 4461, 15, 1_0538, 38, 8, 135, 15, 822, 58, 15, 993, 1_0363, 15, 1460, 8005, 4461, 15, 993, 255, 2328, 9, 9, 9, 6, 26, 1112, 816, 3260, 13, 5, 103, 2377, 6, 17, 1112, 816, 2782, 13, 5, 103, 1_0641, 6, 29, 84, 2512, 2430, 782, 1_8684, 2761, 19, 808, 2430, 2556, 17, 855, 1480, 9477, 4091, 128, 1_1712, 15, 7103, 2153, 673, 17, 2_4883, 9990, 9, 3], [2, 1_1502, 25, 1006, 20, 782, 8, 1_1809, 855, 1732, 1_9393, 1_8667, 37, 367, 2_1018, 69, 1854, 34, 1_1860, 1_9124, 27, 156, 225, 17, 193, 4141, 19, 65, 9124, 9, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 14, 2231, 886, 2385, 1_7659, 84, 14, 1_6792, 1952, 9, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "token_type_ids": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}  # noqa: E501
       # fmt: on

       self.tokenizer_integration_test_util(
           expected_encoding=A_	,							model_name="albert-base-v2"	,							revision="6b6560eaf5ff2e250b00c50f380c5389a9c2d82e"	,							)
