


import json
import os
import pickle
import shutil
import tempfile
from unittest import TestCase
from unittest.mock import patch

import numpy as np
from datasets import Dataset

from transformers import is_faiss_available
from transformers.models.bart.configuration_bart import BartConfig
from transformers.models.bart.tokenization_bart import BartTokenizer
from transformers.models.bert.tokenization_bert import VOCAB_FILES_NAMES as DPR_VOCAB_FILES_NAMES
from transformers.models.dpr.configuration_dpr import DPRConfig
from transformers.models.dpr.tokenization_dpr import DPRContextEncoderTokenizer, DPRQuestionEncoderTokenizer
from transformers.models.rag.configuration_rag import RagConfig
from transformers.models.rag.retrieval_rag import CustomHFIndex, RagRetriever
from transformers.models.roberta.tokenization_roberta import VOCAB_FILES_NAMES as BART_VOCAB_FILES_NAMES
from transformers.testing_utils import require_faiss, require_sentencepiece, require_tokenizers, require_torch


if is_faiss_available():
   import faiss






@require_faiss
class     UpperCAmelCase__       (					__lowerCamelCase		):



    """simple docstring"""






    def _a					(			self    )  ->       int:
         __UpperCamelCase    							=tempfile.mkdtemp()
         __UpperCamelCase    							=8

         # DPR tok
         __UpperCamelCase    							=[
             '[UNK]',
             '[CLS]',
             '[SEP]',
             '[PAD]',
             '[MASK]',
             'want',
             '##want',
             '##ed',
             'wa',
             'un',
             'runn',
             '##ing',
             ',',
             'low',
             'lowest',
         ]
         __UpperCamelCase    							=os.path.join(self.tmpdirname					,   'dpr_tokenizer'    )
         os.makedirs(__A					,   exist_ok=__A    )
         __UpperCamelCase    							=os.path.join(__A					,   DPR_VOCAB_FILES_NAMES['vocab_file']    )
         with open(self.vocab_file					,   'w'					,   encoding='utf-8'    ) as vocab_writer:
              vocab_writer.write(''.join([x + '\n' for x in vocab_tokens]    )    )

         # BART tok
         __UpperCamelCase    							=[
             'l',
             'o',
             'w',
             'e',
             'r',
             's',
             't',
             'i',
             'd',
             'n',
             '\u0120',
             '\u0120l',
             '\u0120n',
             '\u0120lo',
             '\u0120low',
             'er',
             '\u0120lowest',
             '\u0120newer',
             '\u0120wider',
             '<unk>',
         ]
         __UpperCamelCase    							=dict(zip(__A					,   range(len(__A    )    )    )    )
         __UpperCamelCase    							=['#version: 0.2', '\u0120 l', '\u0120l o', '\u0120lo w', 'e r', '']
         __UpperCamelCase    							={'unk_token': '<unk>'}

         __UpperCamelCase    							=os.path.join(self.tmpdirname					,   'bart_tokenizer'    )
         os.makedirs(__A					,   exist_ok=__A    )
         __UpperCamelCase    							=os.path.join(__A					,   BART_VOCAB_FILES_NAMES['vocab_file']    )
         __UpperCamelCase    							=os.path.join(__A					,   BART_VOCAB_FILES_NAMES['merges_file']    )
         with open(self.vocab_file					,   'w'					,   encoding='utf-8'    ) as fp:
              fp.write(json.dumps(__A    ) + '\n'    )
         with open(self.merges_file					,   'w'					,   encoding='utf-8'    ) as fp:
              fp.write('\n'.join(__A    )    )






    def _a					(			self    )  ->       List[str]:
         return DPRQuestionEncoderTokenizer.from_pretrained(os.path.join(self.tmpdirname					,   'dpr_tokenizer'    )    )






    def _a					(			self    )  ->       Union[str, Any]:
         return DPRContextEncoderTokenizer.from_pretrained(os.path.join(self.tmpdirname					,   'dpr_tokenizer'    )    )






    def _a					(			self    )  ->       int:
         return BartTokenizer.from_pretrained(os.path.join(self.tmpdirname					,   'bart_tokenizer'    )    )






    def _a					(			self    )  ->       Dict:
         shutil.rmtree(self.tmpdirname    )






    def _a					(			self    )  ->       str:
         __UpperCamelCase    							=Dataset.from_dict(
             {
                 'id': ['0', '1'],
                 'text': ['foo', 'bar'],
                 'title': ['Foo', 'Bar'],
                 'embeddings': [np.ones(self.retrieval_vector_size    ), 2 * np.ones(self.retrieval_vector_size    )],
             }    )
         dataset.add_faiss_index('embeddings'					,   string_factory='Flat'					,   metric_type=faiss.METRIC_INNER_PRODUCT    )
         return dataset






    def _a					(			self    )  ->       int:
         __UpperCamelCase    							=self.get_dummy_dataset()
         __UpperCamelCase    							=RagConfig(
             retrieval_vector_size=self.retrieval_vector_size					,   question_encoder=DPRConfig().to_dict()					,   generator=BartConfig().to_dict()					,   )
         with patch('transformers.models.rag.retrieval_rag.load_dataset'    ) as mock_load_dataset:
              __UpperCamelCase    							=dataset
              __UpperCamelCase    							=RagRetriever(
                  __A					,   question_encoder_tokenizer=self.get_dpr_tokenizer()					,   generator_tokenizer=self.get_bart_tokenizer()					,   )
         return retriever






    def _a					(			self					,   A_    )  ->       Optional[int]:
         __UpperCamelCase    							=self.get_dummy_dataset()
         __UpperCamelCase    							=RagConfig(
             retrieval_vector_size=self.retrieval_vector_size					,   question_encoder=DPRConfig().to_dict()					,   generator=BartConfig().to_dict()					,   index_name='custom'					,   )
         if from_disk:
              __UpperCamelCase    							=os.path.join(self.tmpdirname					,   'dataset'    )
              __UpperCamelCase    							=os.path.join(self.tmpdirname					,   'index.faiss'    )
              dataset.get_index('embeddings'    ).save(os.path.join(self.tmpdirname					,   'index.faiss'    )    )
              dataset.drop_index('embeddings'    )
              dataset.save_to_disk(os.path.join(self.tmpdirname					,   'dataset'    )    )
              del dataset
              __UpperCamelCase    							=RagRetriever(
                  __A					,   question_encoder_tokenizer=self.get_dpr_tokenizer()					,   generator_tokenizer=self.get_bart_tokenizer()					,   )
         else:
              __UpperCamelCase    							=RagRetriever(
                  __A					,   question_encoder_tokenizer=self.get_dpr_tokenizer()					,   generator_tokenizer=self.get_bart_tokenizer()					,   index=CustomHFIndex(config.retrieval_vector_size					,   __A    )					,   )
         return retriever






    def _a					(			self    )  ->       Union[str, Any]:
         __UpperCamelCase    							=Dataset.from_dict(
             {
                 'id': ['0', '1'],
                 'text': ['foo', 'bar'],
                 'title': ['Foo', 'Bar'],
                 'embeddings': [np.ones(self.retrieval_vector_size + 1    ), 2 * np.ones(self.retrieval_vector_size + 1    )],
             }    )
         dataset.add_faiss_index('embeddings'					,   string_factory='Flat'					,   metric_type=faiss.METRIC_INNER_PRODUCT    )

         __UpperCamelCase    							=os.path.join(self.tmpdirname					,   'hf_bert_base.hnswSQ8_correct_phi_128.c_index'    )
         dataset.save_faiss_index('embeddings'					,   index_file_name + '.index.dpr'    )
         pickle.dump(dataset['id']					,   open(index_file_name + '.index_meta.dpr'					,   'wb'    )    )

         __UpperCamelCase    							=os.path.join(self.tmpdirname					,   'psgs_w100.tsv.pkl'    )
         __UpperCamelCase    							={sample['id']: [sample['text'], sample['title']] for sample in dataset}
         pickle.dump(__A					,   open(__A					,   'wb'    )    )

         __UpperCamelCase    							=RagConfig(
             retrieval_vector_size=self.retrieval_vector_size					,   question_encoder=DPRConfig().to_dict()					,   generator=BartConfig().to_dict()					,   index_name='legacy'					,   index_path=self.tmpdirname					,   )
         __UpperCamelCase    							=RagRetriever(
             __A					,   question_encoder_tokenizer=self.get_dpr_tokenizer()					,   generator_tokenizer=self.get_bart_tokenizer()    )
         return retriever






    def _a					(			self    )  ->       Optional[Any]:
         __UpperCamelCase    							=1
         __UpperCamelCase    							=self.get_dummy_canonical_hf_index_retriever()
         __UpperCamelCase    							=np.array(
             [np.ones(self.retrieval_vector_size    ), -np.ones(self.retrieval_vector_size    )]					,   dtype=np.floataa    )
         __UpperCamelCase							,      __UpperCamelCase							,      __UpperCamelCase    							=retriever.retrieve(__A					,   n_docs=__A    )
         self.assertEqual(retrieved_doc_embeds.shape					,   (2, n_docs, self.retrieval_vector_size)    )
         self.assertEqual(len(__A    )					,   2    )
         self.assertEqual(sorted(doc_dicts[0]    )					,   ['embeddings', 'id', 'text', 'title']    )
         self.assertEqual(len(doc_dicts[0]['id']    )					,   __A    )
         self.assertEqual(doc_dicts[0]['id'][0]					,   '1'    )  # max inner product is reached with second doc
         self.assertEqual(doc_dicts[1]['id'][0]					,   '0'    )  # max inner product is reached with first doc
         self.assertListEqual(doc_ids.tolist()					,   [[1], [0]]    )






    def _a					(			self    )  ->       int:
         __UpperCamelCase    							=self.get_dummy_canonical_hf_index_retriever()
         with tempfile.TemporaryDirectory() as tmp_dirname:
              with patch('transformers.models.rag.retrieval_rag.load_dataset'    ) as mock_load_dataset:
                   __UpperCamelCase    							=self.get_dummy_dataset()
                   retriever.save_pretrained(__A    )
                   __UpperCamelCase    							=RagRetriever.from_pretrained(__A    )
                   self.assertIsInstance(__A					,   __A    )
                   __UpperCamelCase    							=np.array(
                       [np.ones(self.retrieval_vector_size    ), -np.ones(self.retrieval_vector_size    )]					,   dtype=np.floataa    )
                   __UpperCamelCase    							=retriever.retrieve(__A					,   n_docs=1    )
                   self.assertTrue(out is not None    )






    def _a					(			self    )  ->       List[Any]:
         __UpperCamelCase    							=1
         __UpperCamelCase    							=self.get_dummy_custom_hf_index_retriever(from_disk=__A    )
         __UpperCamelCase    							=np.array(
             [np.ones(self.retrieval_vector_size    ), -np.ones(self.retrieval_vector_size    )]					,   dtype=np.floataa    )
         __UpperCamelCase							,      __UpperCamelCase							,      __UpperCamelCase    							=retriever.retrieve(__A					,   n_docs=__A    )
         self.assertEqual(retrieved_doc_embeds.shape					,   (2, n_docs, self.retrieval_vector_size)    )
         self.assertEqual(len(__A    )					,   2    )
         self.assertEqual(sorted(doc_dicts[0]    )					,   ['embeddings', 'id', 'text', 'title']    )
         self.assertEqual(len(doc_dicts[0]['id']    )					,   __A    )
         self.assertEqual(doc_dicts[0]['id'][0]					,   '1'    )  # max inner product is reached with second doc
         self.assertEqual(doc_dicts[1]['id'][0]					,   '0'    )  # max inner product is reached with first doc
         self.assertListEqual(doc_ids.tolist()					,   [[1], [0]]    )






    def _a					(			self    )  ->       Any:
         __UpperCamelCase    							=self.get_dummy_custom_hf_index_retriever(from_disk=__A    )
         with tempfile.TemporaryDirectory() as tmp_dirname:
              retriever.save_pretrained(__A    )
              __UpperCamelCase    							=RagRetriever.from_pretrained(__A    )
              self.assertIsInstance(__A					,   __A    )
              __UpperCamelCase    							=np.array(
                  [np.ones(self.retrieval_vector_size    ), -np.ones(self.retrieval_vector_size    )]					,   dtype=np.floataa    )
              __UpperCamelCase    							=retriever.retrieve(__A					,   n_docs=1    )
              self.assertTrue(out is not None    )






    def _a					(			self    )  ->       List[str]:
         __UpperCamelCase    							=1
         __UpperCamelCase    							=self.get_dummy_custom_hf_index_retriever(from_disk=__A    )
         __UpperCamelCase    							=np.array(
             [np.ones(self.retrieval_vector_size    ), -np.ones(self.retrieval_vector_size    )]					,   dtype=np.floataa    )
         __UpperCamelCase							,      __UpperCamelCase							,      __UpperCamelCase    							=retriever.retrieve(__A					,   n_docs=__A    )
         self.assertEqual(retrieved_doc_embeds.shape					,   (2, n_docs, self.retrieval_vector_size)    )
         self.assertEqual(len(__A    )					,   2    )
         self.assertEqual(sorted(doc_dicts[0]    )					,   ['embeddings', 'id', 'text', 'title']    )
         self.assertEqual(len(doc_dicts[0]['id']    )					,   __A    )
         self.assertEqual(doc_dicts[0]['id'][0]					,   '1'    )  # max inner product is reached with second doc
         self.assertEqual(doc_dicts[1]['id'][0]					,   '0'    )  # max inner product is reached with first doc
         self.assertListEqual(doc_ids.tolist()					,   [[1], [0]]    )






    def _a					(			self    )  ->       Union[str, Any]:
         __UpperCamelCase    							=self.get_dummy_custom_hf_index_retriever(from_disk=__A    )
         with tempfile.TemporaryDirectory() as tmp_dirname:
              retriever.save_pretrained(__A    )
              __UpperCamelCase    							=RagRetriever.from_pretrained(__A    )
              self.assertIsInstance(__A					,   __A    )
              __UpperCamelCase    							=np.array(
                  [np.ones(self.retrieval_vector_size    ), -np.ones(self.retrieval_vector_size    )]					,   dtype=np.floataa    )
              __UpperCamelCase    							=retriever.retrieve(__A					,   n_docs=1    )
              self.assertTrue(out is not None    )






    def _a					(			self    )  ->       str:
         __UpperCamelCase    							=1
         __UpperCamelCase    							=self.get_dummy_legacy_index_retriever()
         __UpperCamelCase    							=np.array(
             [np.ones(self.retrieval_vector_size    ), -np.ones(self.retrieval_vector_size    )]					,   dtype=np.floataa    )
         __UpperCamelCase							,      __UpperCamelCase							,      __UpperCamelCase    							=retriever.retrieve(__A					,   n_docs=__A    )
         self.assertEqual(retrieved_doc_embeds.shape					,   (2, n_docs, self.retrieval_vector_size)    )
         self.assertEqual(len(__A    )					,   2    )
         self.assertEqual(sorted(doc_dicts[0]    )					,   ['text', 'title']    )
         self.assertEqual(len(doc_dicts[0]['text']    )					,   __A    )
         self.assertEqual(doc_dicts[0]['text'][0]					,   'bar'    )  # max inner product is reached with second doc
         self.assertEqual(doc_dicts[1]['text'][0]					,   'foo'    )  # max inner product is reached with first doc
         self.assertListEqual(doc_ids.tolist()					,   [[1], [0]]    )






    def _a					(			self    )  ->       Any:
         __UpperCamelCase    							=self.get_dummy_legacy_index_retriever()
         with tempfile.TemporaryDirectory() as tmp_dirname:
              retriever.save_pretrained(__A    )
              __UpperCamelCase    							=RagRetriever.from_pretrained(__A    )
              self.assertIsInstance(__A					,   __A    )
              __UpperCamelCase    							=np.array(
                  [np.ones(self.retrieval_vector_size    ), -np.ones(self.retrieval_vector_size    )]					,   dtype=np.floataa    )
              __UpperCamelCase    							=retriever.retrieve(__A					,   n_docs=1    )
              self.assertTrue(out is not None    )






    @require_torch
    @require_tokenizers
    @require_sentencepiece
    def _a					(			self    )  ->       Optional[Any]:
         import torch

         __UpperCamelCase    							=1
         __UpperCamelCase    							=self.get_dummy_canonical_hf_index_retriever()
         __UpperCamelCase    							=[[5, 7], [10, 11]]
         __UpperCamelCase    							=np.array(
             [np.ones(self.retrieval_vector_size    ), -np.ones(self.retrieval_vector_size    )]					,   dtype=np.floataa    )
         __UpperCamelCase    							=retriever(__A					,   __A					,   prefix=retriever.config.generator.prefix					,   n_docs=__A    )
         __UpperCamelCase							,      __UpperCamelCase							,      __UpperCamelCase    							=(
             out['context_input_ids'],
             out['context_attention_mask'],
             out['retrieved_doc_embeds'],
         )
         self.assertEqual(retrieved_doc_embeds.shape					,   (2, n_docs, self.retrieval_vector_size)    )
         self.assertIsInstance(__A					,   __A    )
         self.assertIsInstance(__A					,   __A    )
         self.assertIsInstance(__A					,   np.ndarray    )

         __UpperCamelCase    							=retriever(
             __A					,   __A					,   prefix=retriever.config.generator.prefix					,   n_docs=__A					,   return_tensors='pt'					,   )
         __UpperCamelCase							,      __UpperCamelCase							,      __UpperCamelCase							,      __UpperCamelCase    							=(  # noqa: F841
             out['context_input_ids'],
             out['context_attention_mask'],
             out['retrieved_doc_embeds'],
             out['doc_ids'],
         )
         self.assertEqual(retrieved_doc_embeds.shape					,   (2, n_docs, self.retrieval_vector_size)    )
         self.assertIsInstance(__A					,   torch.Tensor    )
         self.assertIsInstance(__A					,   torch.Tensor    )
         self.assertIsInstance(__A					,   torch.Tensor    )






    @require_torch
    @require_tokenizers
    @require_sentencepiece
    def _a					(			self    )  ->       Tuple:
         __UpperCamelCase    							=self.get_dpr_ctx_encoder_tokenizer()
         __UpperCamelCase    							=1
         __UpperCamelCase    							=self.get_dummy_custom_hf_index_retriever(from_disk=__A    )
         retriever.set_ctx_encoder_tokenizer(__A    )

         __UpperCamelCase    							=[[5, 7], [10, 11]]
         __UpperCamelCase    							=np.array(
             [np.ones(self.retrieval_vector_size    ), -np.ones(self.retrieval_vector_size    )]					,   dtype=np.floataa    )
         __UpperCamelCase    							=retriever(__A					,   __A					,   prefix=retriever.config.generator.prefix					,   n_docs=__A    )

         self.assertEqual(
             len(__A    )					,   6    )  # check whether the retriever output consist of 6 attributes including tokenized docs
         self.assertEqual(
             all(k in out for k in ('tokenized_doc_ids', 'tokenized_doc_attention_mask')    )					,   __A    )  # check for doc token related keys in dictionary.












'''simple docstring'''
from __future__ import annotations

class      snake_case     :




 """simple docstring"""



 def __init__(       self       :							Optional[int]							,	__A       :							list[list[int]]	):
        __UpperCamelCase       =  TypeError(
            'Matrices must be formed from a list of zero or more lists containing at '
            'least one and the same number of values, each of which must be of type '
            'int or float.'	)
        if len(__A	) != 0:
               __UpperCamelCase       =  len(rows[0]	)
               if cols == 0:
                      raise error
               for row in rows:
                      if len(__A	) != cols:
                             raise error
                      for value in row:
                             if not isinstance(__A							,	(int, float)	):
                                    raise error
               __UpperCamelCase       =  rows
        else:
               __UpperCamelCase       =  []






 def        _lowerCamelCase					(       self       :							int	):
        return [[row[i] for row in self.rows] for i in range(len(self.rows[0]	)	)]






 @property
 def        _lowerCamelCase					(       self       :							str	):
        return len(self.rows	)






 @property
 def        _lowerCamelCase					(       self       :							Any	):
        return len(self.rows[0]	)






 @property
 def        _lowerCamelCase					(       self       :							Optional[Any]	):
        return (self.num_rows, self.num_columns)






 @property
 def        _lowerCamelCase					(       self       :							Dict	):
        return self.order[0] == self.order[1]






 def        _lowerCamelCase					(       self       :							Any	):
        __UpperCamelCase       =  [
            [0 if column_num != row_num else 1 for column_num in range(self.num_rows	)]
            for row_num in range(self.num_rows	)
        ]
        return Matrix(__A	)






 def        _lowerCamelCase					(       self       :							Any	):
        if not self.is_square:
               return 0
        if self.order == (0, 0):
               return 1
        if self.order == (1, 1):
               return int(self.rows[0][0]	)
        if self.order == (2, 2):
               return int(
                   (self.rows[0][0] * self.rows[1][1])
                   - (self.rows[0][1] * self.rows[1][0])	)
        else:
               return sum(
                   self.rows[0][column] * self.cofactors().rows[0][column]
                   for column in range(self.num_columns	)	)






 def        _lowerCamelCase					(       self       :							List[str]	):
        return bool(self.determinant()	)






 def        _lowerCamelCase					(       self       :							Dict							,	__A       :							int							,	__A       :							int	):
        __UpperCamelCase       =  [
            [
                self.rows[other_row][other_column]
                for other_column in range(self.num_columns	)
                if other_column != column
            ]
            for other_row in range(self.num_rows	)
            if other_row != row
        ]
        return Matrix(__A	).determinant()






 def        _lowerCamelCase					(       self       :							Dict							,	__A       :							int							,	__A       :							int	):
        if (row + column) % 2 == 0:
               return self.get_minor(__A							,	__A	)
        return -1 * self.get_minor(__A							,	__A	)






 def        _lowerCamelCase					(       self       :							List[str]	):
        return Matrix(
            [
                [self.get_minor(__A							,	__A	) for column in range(self.num_columns	)]
                for row in range(self.num_rows	)
            ]	)






 def        _lowerCamelCase					(       self       :							Union[str, Any]	):
        return Matrix(
            [
                [
                    self.minors().rows[row][column]
                    if (row + column) % 2 == 0
                    else self.minors().rows[row][column] * -1
                    for column in range(self.minors().num_columns	)
                ]
                for row in range(self.minors().num_rows	)
            ]	)






 def        _lowerCamelCase					(       self       :							List[str]	):
        __UpperCamelCase       =  [
            [self.cofactors().rows[column][row] for column in range(self.num_columns	)]
            for row in range(self.num_rows	)
        ]
        return Matrix(__A	)






 def        _lowerCamelCase					(       self       :							Dict	):
        __UpperCamelCase       =  self.determinant()
        if not determinant:
               raise TypeError('Only matrices with a non-zero determinant have an inverse'	)
        return self.adjugate() * (1 / determinant)






 def __repr__(       self       :							Optional[Any]	):
        return str(self.rows	)






 def __str__(       self       :							Union[str, Any]	):
        if self.num_rows == 0:
               return "[]"
        if self.num_rows == 1:
               return "[[" + ". ".join(str(self.rows[0]	)	) + "]]"
        return (
            "["
            + "\n ".join(
                [
                    '[' + '. '.join([str(__A	) for value in row]	) + '.]'
                    for row in self.rows
                ]	)
            + "]"
        )






 def        _lowerCamelCase					(       self       :							List[Any]							,	__A       :							list[int]							,	__A       :							int | None = None	):
        __UpperCamelCase       =  TypeError('Row must be a list containing all ints and/or floats'	)
        if not isinstance(__A							,	__A	):
               raise type_error
        for value in row:
               if not isinstance(__A							,	(int, float)	):
                      raise type_error
        if len(__A	) != self.num_columns:
               raise ValueError(
                   'Row must be equal in length to the other rows in the matrix'	)
        if position is None:
               self.rows.append(__A	)
        else:
               __UpperCamelCase       =  self.rows[0:position] + [row] + self.rows[position:]






 def        _lowerCamelCase					(       self       :							Optional[Any]							,	__A       :							list[int]							,	__A       :							int | None = None	):
        __UpperCamelCase       =  TypeError(
            'Column must be a list containing all ints and/or floats'	)
        if not isinstance(__A							,	__A	):
               raise type_error
        for value in column:
               if not isinstance(__A							,	(int, float)	):
                      raise type_error
        if len(__A	) != self.num_rows:
               raise ValueError(
                   'Column must be equal in length to the other columns in the matrix'	)
        if position is None:
               __UpperCamelCase       =  [self.rows[i] + [column[i]] for i in range(self.num_rows	)]
        else:
               __UpperCamelCase       =  [
                   self.rows[i][0:position] + [column[i]] + self.rows[i][position:]
                   for i in range(self.num_rows	)
               ]






 def __eq__(       self       :							Tuple							,	__A       :							object	):
        if not isinstance(__A							,	__A	):
               return NotImplemented
        return self.rows == other.rows






 def __ne__(       self       :							Any							,	__A       :							object	):
        return not self == other






 def __neg__(       self       :							List[Any]	):
        return self * -1






 def __add__(       self       :							List[str]							,	__A       :							Matrix	):
        if self.order != other.order:
               raise ValueError('Addition requires matrices of the same order'	)
        return Matrix(
            [
                [self.rows[i][j] + other.rows[i][j] for j in range(self.num_columns	)]
                for i in range(self.num_rows	)
            ]	)






 def __sub__(       self       :							str							,	__A       :							Matrix	):
        if self.order != other.order:
               raise ValueError('Subtraction requires matrices of the same order'	)
        return Matrix(
            [
                [self.rows[i][j] - other.rows[i][j] for j in range(self.num_columns	)]
                for i in range(self.num_rows	)
            ]	)






 def __mul__(       self       :							str							,	__A       :							Matrix | int | float	):
        if isinstance(__A							,	(int, float)	):
               return Matrix(
                   [[int(element * other	) for element in row] for row in self.rows]	)
        elif isinstance(__A							,	__A	):
               if self.num_columns != other.num_rows:
                      raise ValueError(
                          'The number of columns in the first matrix must '
                          'be equal to the number of rows in the second'	)
               return Matrix(
                   [
                       [Matrix.dot_product(__A							,	__A	) for column in other.columns()]
                       for row in self.rows
                   ]	)
        else:
               raise TypeError(
                   'A Matrix can only be multiplied by an int, float, or another matrix'	)






 def __pow__(       self       :							Union[str, Any]							,	__A       :							int	):
        if not isinstance(__A							,	__A	):
               raise TypeError('A Matrix can only be raised to the power of an int'	)
        if not self.is_square:
               raise ValueError('Only square matrices can be raised to a power'	)
        if other == 0:
               return self.identity()
        if other < 0:
               if self.is_invertable():
                      return self.inverse() ** (-other)
               raise ValueError(
                   'Only invertable matrices can be raised to a negative power'	)
        __UpperCamelCase       =  self
        for _ in range(other - 1	):
               result *= self
        return result






 @classmethod
 def        _lowerCamelCase					(       cls       :							Tuple							,	__A       :							list[int]							,	__A       :							list[int]	):
        return sum(row[i] * column[i] for i in range(len(__A	)	)	)


if __name__ == "__main__":
    import doctest

    doctest.testmod()
