


"""simple docstring"""







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_	( UpperCamelCase):

	"""simple docstring"""





	def   UpperCAmelCase_      ( self			:				List[str]   )       ->	str:
						__SCREAMING_SNAKE_CASE						   =				tempfile.mkdtemp()
						__SCREAMING_SNAKE_CASE						   =				8

						# DPR tok
						__SCREAMING_SNAKE_CASE						   =				[
						    "[UNK]",
						    "[CLS]",
						    "[SEP]",
						    "[PAD]",
						    "[MASK]",
						    "want",
						    "##want",
						    "##ed",
						    "wa",
						    "un",
						    "runn",
						    "##ing",
						    ",",
						    "low",
						    "lowest",
						]
						__SCREAMING_SNAKE_CASE						   =				os.path.join(self.tmpdirname			,			"dpr_tokenizer"   )
						os.makedirs(UpperCAmelCase__			,			exist_ok=UpperCAmelCase__   )
						__SCREAMING_SNAKE_CASE						   =				os.path.join(UpperCAmelCase__			,			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
						__SCREAMING_SNAKE_CASE						   =				[
						    "l",
						    "o",
						    "w",
						    "e",
						    "r",
						    "s",
						    "t",
						    "i",
						    "d",
						    "n",
						    "\u0120",
						    "\u0120l",
						    "\u0120n",
						    "\u0120lo",
						    "\u0120low",
						    "er",
						    "\u0120lowest",
						    "\u0120newer",
						    "\u0120wider",
						    "<unk>",
						]
						__SCREAMING_SNAKE_CASE						   =				dict(zip(UpperCAmelCase__			,			range(len(UpperCAmelCase__   )   )   )   )
						__SCREAMING_SNAKE_CASE						   =				["#version: 0.2", "\u0120 l", "\u0120l o", "\u0120lo w", "e r", ""]
						__SCREAMING_SNAKE_CASE						   =				{"unk_token": "<unk>"}

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




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




	def   UpperCAmelCase_      ( self			:				Tuple   )       ->	DPRContextEncoderTokenizer:
						return DPRContextEncoderTokenizer.from_pretrained(os.path.join(self.tmpdirname			,			"dpr_tokenizer"   )   )




	def   UpperCAmelCase_      ( self			:				Tuple   )       ->	BartTokenizer:
						return BartTokenizer.from_pretrained(os.path.join(self.tmpdirname			,			"bart_tokenizer"   )   )




	def   UpperCAmelCase_      ( self			:				int   )       ->	Union[str, Any]:
						shutil.rmtree(self.tmpdirname   )




	def   UpperCAmelCase_      ( self			:				List[str]   )       ->	str:
						__SCREAMING_SNAKE_CASE						   =				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   UpperCAmelCase_      ( self			:				Any   )       ->	Union[str, Any]:
						__SCREAMING_SNAKE_CASE						   =				self.get_dummy_dataset()
						__SCREAMING_SNAKE_CASE						   =				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:
											__SCREAMING_SNAKE_CASE						   =				dataset
											__SCREAMING_SNAKE_CASE						   =				RagRetriever(
											    UpperCAmelCase__			,			question_encoder_tokenizer=self.get_dpr_tokenizer()			,			generator_tokenizer=self.get_bart_tokenizer()			,			)
						return retriever




	def   UpperCAmelCase_      ( self			:				int			,			UpperCAmelCase__			:				bool   )       ->	Optional[int]:
						__SCREAMING_SNAKE_CASE						   =				self.get_dummy_dataset()
						__SCREAMING_SNAKE_CASE						   =				RagConfig(
						    retrieval_vector_size=self.retrieval_vector_size			,			question_encoder=DPRConfig().to_dict()			,			generator=BartConfig().to_dict()			,			index_name="custom"			,			)
						if from_disk:
											__SCREAMING_SNAKE_CASE						   =				os.path.join(self.tmpdirname			,			"dataset"   )
											__SCREAMING_SNAKE_CASE						   =				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
											__SCREAMING_SNAKE_CASE						   =				RagRetriever(
											    UpperCAmelCase__			,			question_encoder_tokenizer=self.get_dpr_tokenizer()			,			generator_tokenizer=self.get_bart_tokenizer()			,			)
						else:
											__SCREAMING_SNAKE_CASE						   =				RagRetriever(
											    UpperCAmelCase__			,			question_encoder_tokenizer=self.get_dpr_tokenizer()			,			generator_tokenizer=self.get_bart_tokenizer()			,			index=CustomHFIndex(config.retrieval_vector_size			,			UpperCAmelCase__   )			,			)
						return retriever




	def   UpperCAmelCase_      ( self			:				Union[str, Any]   )       ->	Optional[Any]:
						__SCREAMING_SNAKE_CASE						   =				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   )

						__SCREAMING_SNAKE_CASE						   =				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"   )   )

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

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




	def   UpperCAmelCase_      ( self			:				Optional[Any]   )       ->	Optional[Any]:
						__SCREAMING_SNAKE_CASE						   =				1
						__SCREAMING_SNAKE_CASE						   =				self.get_dummy_canonical_hf_index_retriever()
						__SCREAMING_SNAKE_CASE						   =				np.array(
						    [np.ones(self.retrieval_vector_size   ), -np.ones(self.retrieval_vector_size   )]			,			dtype=np.floataa   )
						__SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE						   =				retriever.retrieve(UpperCAmelCase__			,			n_docs=UpperCAmelCase__   )
						self.assertEqual(retrieved_doc_embeds.shape			,			(2, n_docs, self.retrieval_vector_size)   )
						self.assertEqual(len(UpperCAmelCase__   )			,			2   )
						self.assertEqual(sorted(doc_dicts[0]   )			,			["embeddings", "id", "text", "title"]   )
						self.assertEqual(len(doc_dicts[0]["id"]   )			,			UpperCAmelCase__   )
						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   UpperCAmelCase_      ( self			:				Dict   )       ->	Optional[int]:
						__SCREAMING_SNAKE_CASE						   =				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:
																__SCREAMING_SNAKE_CASE						   =				self.get_dummy_dataset()
																retriever.save_pretrained(UpperCAmelCase__   )
																__SCREAMING_SNAKE_CASE						   =				RagRetriever.from_pretrained(UpperCAmelCase__   )
																self.assertIsInstance(UpperCAmelCase__			,			UpperCAmelCase__   )
																__SCREAMING_SNAKE_CASE						   =				np.array(
																    [np.ones(self.retrieval_vector_size   ), -np.ones(self.retrieval_vector_size   )]			,			dtype=np.floataa   )
																__SCREAMING_SNAKE_CASE						   =				retriever.retrieve(UpperCAmelCase__			,			n_docs=1   )
																self.assertTrue(out is not None   )




	def   UpperCAmelCase_      ( self			:				Union[str, Any]   )       ->	List[Any]:
						__SCREAMING_SNAKE_CASE						   =				1
						__SCREAMING_SNAKE_CASE						   =				self.get_dummy_custom_hf_index_retriever(from_disk=UpperCAmelCase__   )
						__SCREAMING_SNAKE_CASE						   =				np.array(
						    [np.ones(self.retrieval_vector_size   ), -np.ones(self.retrieval_vector_size   )]			,			dtype=np.floataa   )
						__SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE						   =				retriever.retrieve(UpperCAmelCase__			,			n_docs=UpperCAmelCase__   )
						self.assertEqual(retrieved_doc_embeds.shape			,			(2, n_docs, self.retrieval_vector_size)   )
						self.assertEqual(len(UpperCAmelCase__   )			,			2   )
						self.assertEqual(sorted(doc_dicts[0]   )			,			["embeddings", "id", "text", "title"]   )
						self.assertEqual(len(doc_dicts[0]["id"]   )			,			UpperCAmelCase__   )
						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   UpperCAmelCase_      ( self			:				Tuple   )       ->	Dict:
						__SCREAMING_SNAKE_CASE						   =				self.get_dummy_custom_hf_index_retriever(from_disk=UpperCAmelCase__   )
						with tempfile.TemporaryDirectory() as tmp_dirname:
											retriever.save_pretrained(UpperCAmelCase__   )
											__SCREAMING_SNAKE_CASE						   =				RagRetriever.from_pretrained(UpperCAmelCase__   )
											self.assertIsInstance(UpperCAmelCase__			,			UpperCAmelCase__   )
											__SCREAMING_SNAKE_CASE						   =				np.array(
											    [np.ones(self.retrieval_vector_size   ), -np.ones(self.retrieval_vector_size   )]			,			dtype=np.floataa   )
											__SCREAMING_SNAKE_CASE						   =				retriever.retrieve(UpperCAmelCase__			,			n_docs=1   )
											self.assertTrue(out is not None   )




	def   UpperCAmelCase_      ( self			:				List[str]   )       ->	Any:
						__SCREAMING_SNAKE_CASE						   =				1
						__SCREAMING_SNAKE_CASE						   =				self.get_dummy_custom_hf_index_retriever(from_disk=UpperCAmelCase__   )
						__SCREAMING_SNAKE_CASE						   =				np.array(
						    [np.ones(self.retrieval_vector_size   ), -np.ones(self.retrieval_vector_size   )]			,			dtype=np.floataa   )
						__SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE						   =				retriever.retrieve(UpperCAmelCase__			,			n_docs=UpperCAmelCase__   )
						self.assertEqual(retrieved_doc_embeds.shape			,			(2, n_docs, self.retrieval_vector_size)   )
						self.assertEqual(len(UpperCAmelCase__   )			,			2   )
						self.assertEqual(sorted(doc_dicts[0]   )			,			["embeddings", "id", "text", "title"]   )
						self.assertEqual(len(doc_dicts[0]["id"]   )			,			UpperCAmelCase__   )
						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   UpperCAmelCase_      ( self			:				int   )       ->	List[Any]:
						__SCREAMING_SNAKE_CASE						   =				self.get_dummy_custom_hf_index_retriever(from_disk=UpperCAmelCase__   )
						with tempfile.TemporaryDirectory() as tmp_dirname:
											retriever.save_pretrained(UpperCAmelCase__   )
											__SCREAMING_SNAKE_CASE						   =				RagRetriever.from_pretrained(UpperCAmelCase__   )
											self.assertIsInstance(UpperCAmelCase__			,			UpperCAmelCase__   )
											__SCREAMING_SNAKE_CASE						   =				np.array(
											    [np.ones(self.retrieval_vector_size   ), -np.ones(self.retrieval_vector_size   )]			,			dtype=np.floataa   )
											__SCREAMING_SNAKE_CASE						   =				retriever.retrieve(UpperCAmelCase__			,			n_docs=1   )
											self.assertTrue(out is not None   )




	def   UpperCAmelCase_      ( self			:				List[str]   )       ->	int:
						__SCREAMING_SNAKE_CASE						   =				1
						__SCREAMING_SNAKE_CASE						   =				self.get_dummy_legacy_index_retriever()
						__SCREAMING_SNAKE_CASE						   =				np.array(
						    [np.ones(self.retrieval_vector_size   ), -np.ones(self.retrieval_vector_size   )]			,			dtype=np.floataa   )
						__SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE						   =				retriever.retrieve(UpperCAmelCase__			,			n_docs=UpperCAmelCase__   )
						self.assertEqual(retrieved_doc_embeds.shape			,			(2, n_docs, self.retrieval_vector_size)   )
						self.assertEqual(len(UpperCAmelCase__   )			,			2   )
						self.assertEqual(sorted(doc_dicts[0]   )			,			["text", "title"]   )
						self.assertEqual(len(doc_dicts[0]["text"]   )			,			UpperCAmelCase__   )
						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   UpperCAmelCase_      ( self			:				str   )       ->	List[Any]:
						__SCREAMING_SNAKE_CASE						   =				self.get_dummy_legacy_index_retriever()
						with tempfile.TemporaryDirectory() as tmp_dirname:
											retriever.save_pretrained(UpperCAmelCase__   )
											__SCREAMING_SNAKE_CASE						   =				RagRetriever.from_pretrained(UpperCAmelCase__   )
											self.assertIsInstance(UpperCAmelCase__			,			UpperCAmelCase__   )
											__SCREAMING_SNAKE_CASE						   =				np.array(
											    [np.ones(self.retrieval_vector_size   ), -np.ones(self.retrieval_vector_size   )]			,			dtype=np.floataa   )
											__SCREAMING_SNAKE_CASE						   =				retriever.retrieve(UpperCAmelCase__			,			n_docs=1   )
											self.assertTrue(out is not None   )




	@require_torch
	@require_tokenizers
	@require_sentencepiece
	def   UpperCAmelCase_      ( self			:				Dict   )       ->	int:
						import torch

						__SCREAMING_SNAKE_CASE						   =				1
						__SCREAMING_SNAKE_CASE						   =				self.get_dummy_canonical_hf_index_retriever()
						__SCREAMING_SNAKE_CASE						   =				[[5, 7], [1_0, 1_1]]
						__SCREAMING_SNAKE_CASE						   =				np.array(
						    [np.ones(self.retrieval_vector_size   ), -np.ones(self.retrieval_vector_size   )]			,			dtype=np.floataa   )
						__SCREAMING_SNAKE_CASE						   =				retriever(UpperCAmelCase__			,			UpperCAmelCase__			,			prefix=retriever.config.generator.prefix			,			n_docs=UpperCAmelCase__   )
						__SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE						   =				(
						    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(UpperCAmelCase__			,			UpperCAmelCase__   )
						self.assertIsInstance(UpperCAmelCase__			,			UpperCAmelCase__   )
						self.assertIsInstance(UpperCAmelCase__			,			np.ndarray   )

						__SCREAMING_SNAKE_CASE						   =				retriever(
						    UpperCAmelCase__			,			UpperCAmelCase__			,			prefix=retriever.config.generator.prefix			,			n_docs=UpperCAmelCase__			,			return_tensors="pt"			,			)
						__SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE						   =				(  # 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(UpperCAmelCase__			,			torch.Tensor   )
						self.assertIsInstance(UpperCAmelCase__			,			torch.Tensor   )
						self.assertIsInstance(UpperCAmelCase__			,			torch.Tensor   )




	@require_torch
	@require_tokenizers
	@require_sentencepiece
	def   UpperCAmelCase_      ( self			:				str   )       ->	Optional[int]:
						__SCREAMING_SNAKE_CASE						   =				self.get_dpr_ctx_encoder_tokenizer()
						__SCREAMING_SNAKE_CASE						   =				1
						__SCREAMING_SNAKE_CASE						   =				self.get_dummy_custom_hf_index_retriever(from_disk=UpperCAmelCase__   )
						retriever.set_ctx_encoder_tokenizer(UpperCAmelCase__   )

						__SCREAMING_SNAKE_CASE						   =				[[5, 7], [1_0, 1_1]]
						__SCREAMING_SNAKE_CASE						   =				np.array(
						    [np.ones(self.retrieval_vector_size   ), -np.ones(self.retrieval_vector_size   )]			,			dtype=np.floataa   )
						__SCREAMING_SNAKE_CASE						   =				retriever(UpperCAmelCase__			,			UpperCAmelCase__			,			prefix=retriever.config.generator.prefix			,			n_docs=UpperCAmelCase__   )

						self.assertEqual(
						    len(UpperCAmelCase__   )			,			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")   )			,			UpperCAmelCase__   )  # check for doc token related keys in dictionary.



from __future__ import annotations

from typing import Any


class       SCREAMING_SNAKE_CASE__					:





    def __init__(      self						,   a						,   a						,   a = 0):
         lowercase__      , lowercase__    :   Dict      =       row, column
         lowercase__    :   Optional[Any]      =       [[default_value for c in range(a)] for r in range(a)]





    def __str__(      self):
         lowercase__    :   Tuple      =       f"""Matrix consist of {self.row} rows and {self.column} columns\n"""

         # Make string identifier
         lowercase__    :   Optional[int]      =       0
         for row_vector in self.array:
              for obj in row_vector:
                   lowercase__    :   List[str]      =       max(a						,   len(str(a)))
         lowercase__    :   Optional[int]      =       f"""%{max_element_length}s"""

         # Make string and return
         def single_line(a) -> str:
              nonlocal string_format_identifier
              lowercase__    :   Tuple      =       '['
              line += ", ".join(string_format_identifier % (obj,) for obj in row_vector)
              line += "]"
              return line

         s += "\n".join(single_line(a) for row_vector in self.array)
         return s





    def __repr__(      self):
         return str(self)





    def       snake_case_				(      self						,   a):
         if not (isinstance(a						,   (list, tuple)) and len(a) == 2):
              return False
         elif not (0 <= loc[0] < self.row and 0 <= loc[1] < self.column):
              return False
         else:
              return True





    def __getitem__(      self						,   a):
         assert self.validate_indicies(a)
         return self.array[loc[0]][loc[1]]





    def __setitem__(      self						,   a						,   a):
         assert self.validate_indicies(a)
         lowercase__    :   List[str]      =       value





    def __add__(      self						,   a):
         assert isinstance(a						,   a)
         assert self.row == another.row and self.column == another.column

         # Add
         lowercase__    :   List[str]      =       Matrix(self.row						,   self.column)
         for r in range(self.row):
              for c in range(self.column):
                   lowercase__    :   Dict      =       self[r, c] + another[r, c]
         return result





    def __neg__(      self):
         lowercase__    :   List[Any]      =       Matrix(self.row						,   self.column)
         for r in range(self.row):
              for c in range(self.column):
                   lowercase__    :   int      =       -self[r, c]
         return result





    def __sub__(      self						,   a):
         return self + (-another)





    def __mul__(      self						,   a):

         if isinstance(a						,   (int, float)):  # Scalar multiplication
              lowercase__    :   Optional[Any]      =       Matrix(self.row						,   self.column)
              for r in range(self.row):
                   for c in range(self.column):
                        lowercase__    :   Union[str, Any]      =       self[r, c] * another
              return result
         elif isinstance(a						,   a):  # Matrix multiplication
              assert self.column == another.row
              lowercase__    :   List[Any]      =       Matrix(self.row						,   another.column)
              for r in range(self.row):
                   for c in range(another.column):
                        for i in range(self.column):
                             result[r, c] += self[r, i] * another[i, c]
              return result
         else:
              lowercase__    :   Optional[Any]      =       f"""Unsupported type given for another ({type(a)})"""
              raise TypeError(a)





    def       snake_case_				(      self):
         lowercase__    :   Optional[int]      =       Matrix(self.column						,   self.row)
         for r in range(self.row):
              for c in range(self.column):
                   lowercase__    :   str      =       self[r, c]
         return result





    def       snake_case_				(      self						,   a						,   a):
         assert isinstance(a						,   a) and isinstance(a						,   a)
         assert self.row == self.column == u.row == v.row  # u, v should be column vector
         assert u.column == v.column == 1  # u, v should be column vector

         # Calculate
         lowercase__    :   int      =       v.transpose()
         lowercase__    :   Tuple      =       (v_t * self * u)[0, 0] + 1
         if numerator_factor == 0:
              return None  # It's not invertable
         return self - ((self * u) * (v_t * self) * (1.0 / numerator_factor))


# Testing
if __name__ == "__main__":

       def 	snake_case__			(    ):



            '''simple docstring'''





            lowercase__    :   Any      =       Matrix(3	,     3	,     0			)
            for i in range(3			):
                 lowercase__    :   str      =       1
            print(f"""a^(-1) is {ainv}"""			)
            # u, v
            lowercase__    :   Optional[Any]      =       Matrix(3	,     1	,     0			)
            lowercase__      , lowercase__      , lowercase__    :   List[Any]      =       1, 2, -3
            lowercase__    :   Union[str, Any]      =       Matrix(3	,     1	,     0			)
            lowercase__      , lowercase__      , lowercase__    :   Any      =       4, -2, 5
            print(f"""u is {u}"""			)
            print(f"""v is {v}"""			)
            print(f"""uv^T is {u * v.transpose()}"""			)
            # Sherman Morrison
            print(f"""(a + uv^T)^(-1) is {ainv.sherman_morrison(SCREAMING_SNAKE_CASE_	,     SCREAMING_SNAKE_CASE_			)}"""			)

       def 	snake_case__			(    ):



            '''simple docstring'''





            import doctest

            doctest.testmod()

       testa()

