code: 
  '''simple docstring'''
  
  import json
  import os
  import shutil
  import sys
  import tempfile
  import unittest
  from unittest import TestCase
  from unittest.mock import patch
  
  import faiss
  import numpy as np
  from datasets import Dataset
  
  from transformers import BartConfig, BartTokenizer, DPRConfig, DPRQuestionEncoderTokenizer, RagConfig
  from transformers.file_utils import is_datasets_available, is_faiss_available, is_psutil_available, is_torch_available
  from transformers.integrations import is_ray_available
  from transformers.models.bert.tokenization_bert import VOCAB_FILES_NAMES as DPR_VOCAB_FILES_NAMES
  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_ray
  
  
  sys.path.append(os.path.join(os.getcwd()))  # noqa: E402 # noqa: E402 # isort:skip
  
  if is_torch_available():
       from distributed_pytorch_retriever import RagPyTorchDistributedRetriever  # noqa: E402 # isort:skip
  else:
       UpperCamelCase_     			=       None
  
  if is_ray_available():
       import ray  # noqa: E402 # isort:skip
       from distributed_ray_retriever import RagRayDistributedRetriever, RayRetriever  # noqa: E402 # isort:skip
  else:
       UpperCamelCase_     			=       None
       UpperCamelCase_     			=       None
       UpperCamelCase_     			=       None
  
  
  def 	_UpperCAmelCase				(  _lowerCamelCase						:       Union[str, Any]		)    ->						Optional[Any]:
    if not (is_datasets_available() and is_faiss_available() and is_psutil_available()):
      _lowerCAmelCase       :  Union[str, Any]   				=					unittest.skip("""test requires Datasets, Faiss, psutil"""		)(_lowerCamelCase		)
    return test_case
  
  
  
  @require_distributed_retrieval
  class   a_  (_a    ):
  
  
  
  
         def 							__UpperCamelCase       (     self  ):
           _lowerCAmelCase       :  Tuple   				=					tempfile.mkdtemp()
           _lowerCAmelCase       :  int   				=					8
  
           # DPR tok
           _lowerCAmelCase       :  Optional[Any]   				=					[
               """[UNK]""",
               """[CLS]""",
               """[SEP]""",
               """[PAD]""",
               """[MASK]""",
               """want""",
               """##want""",
               """##ed""",
               """wa""",
               """un""",
               """runn""",
               """##ing""",
               """,""",
               """low""",
               """lowest""",
           ]
           _lowerCAmelCase       :  List[str]   				=					os.path.join(self.tmpdirname   ,   """dpr_tokenizer"""  )
           os.makedirs(snake_case_   ,   exist_ok=snake_case_  )
           _lowerCAmelCase       :  Dict   				=					os.path.join(snake_case_   ,   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
           _lowerCAmelCase       :  str   				=					[
               """l""",
               """o""",
               """w""",
               """e""",
               """r""",
               """s""",
               """t""",
               """i""",
               """d""",
               """n""",
               """\u0120""",
               """\u0120l""",
               """\u0120n""",
               """\u0120lo""",
               """\u0120low""",
               """er""",
               """\u0120lowest""",
               """\u0120newer""",
               """\u0120wider""",
               """<unk>""",
           ]
           _lowerCAmelCase       :  Union[str, Any]   				=					dict(zip(snake_case_   ,   range(len(snake_case_  )  )  )  )
           _lowerCAmelCase       :  List[Any]   				=					["""#version: 0.2""", """\u0120 l""", """\u0120l o""", """\u0120lo w""", """e r""", """"""]
           _lowerCAmelCase       :  Optional[Any]   				=					{"""unk_token""": """<unk>"""}
  
           _lowerCAmelCase       :  Tuple   				=					os.path.join(self.tmpdirname   ,   """bart_tokenizer"""  )
           os.makedirs(snake_case_   ,   exist_ok=snake_case_  )
           _lowerCAmelCase       :  str   				=					os.path.join(snake_case_   ,   BART_VOCAB_FILES_NAMES["""vocab_file"""]  )
           _lowerCAmelCase       :  Any   				=					os.path.join(snake_case_   ,   BART_VOCAB_FILES_NAMES["""merges_file"""]  )
           with open(self.vocab_file   ,   """w"""   ,   encoding="""utf-8"""  ) as fp:
             fp.write(json.dumps(snake_case_  ) + """\n"""  )
           with open(self.merges_file   ,   """w"""   ,   encoding="""utf-8"""  ) as fp:
             fp.write("""\n""".join(snake_case_  )  )
  
  
  
  
         def 							__UpperCamelCase       (     self  ):
           return DPRQuestionEncoderTokenizer.from_pretrained(os.path.join(self.tmpdirname   ,   """dpr_tokenizer"""  )  )
  
  
  
  
         def 							__UpperCamelCase       (     self  ):
           return BartTokenizer.from_pretrained(os.path.join(self.tmpdirname   ,   """bart_tokenizer"""  )  )
  
  
  
  
         def 							__UpperCamelCase       (     self  ):
           shutil.rmtree(self.tmpdirname  )
  
  
  
  
         def 							__UpperCamelCase       (     self  ):
           _lowerCAmelCase       :  Tuple   				=					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   ,   snake_case_   ,   snake_case_=1_2_3_4_5  ):
           _lowerCAmelCase       :  List[str]   				=					self.get_dummy_dataset()
           _lowerCAmelCase       :  Union[str, Any]   				=					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:
             _lowerCAmelCase       :  Dict   				=					dataset
             _lowerCAmelCase       :  Optional[Any]   				=					RagPyTorchDistributedRetriever(
                 snake_case_   ,   question_encoder_tokenizer=self.get_dpr_tokenizer()   ,   generator_tokenizer=self.get_bart_tokenizer()   ,   )
             if init_retrieval:
               retriever.init_retrieval(snake_case_  )
           return retriever
  
  
  
  
         def 							__UpperCamelCase       (     self   ,   snake_case_  ):
           # Have to run in local mode because sys.path modifications at top of
           # file are not propogated to remote workers.
           # https://stackoverflow.com/questions/54338013/parallel-import-a-python-file-from-sibling-folder
           ray.init(local_mode=snake_case_  )
           _lowerCAmelCase       :  Dict   				=					RagConfig(
               retrieval_vector_size=self.retrieval_vector_size   ,   question_encoder=DPRConfig().to_dict()   ,   generator=BartConfig().to_dict()   ,   )
           _lowerCAmelCase       :  Union[str, Any]   				=					ray.remote(snake_case_  )
           _lowerCAmelCase       :  int   				=					[remote_cls.remote() for _ in range(1  )]
           with patch("""transformers.models.rag.retrieval_rag.load_dataset"""  ) as mock_load_dataset:
             _lowerCAmelCase       :  str   				=					self.get_dummy_dataset()
             _lowerCAmelCase       :  int   				=					RagRayDistributedRetriever(
                 snake_case_   ,   question_encoder_tokenizer=self.get_dpr_tokenizer()   ,   generator_tokenizer=self.get_bart_tokenizer()   ,   retrieval_workers=snake_case_   ,   )
             if init_retrieval:
               retriever.init_retrieval()
           return retriever
  
  
  
  
         def 							__UpperCamelCase       (     self   ,   snake_case_   ,   snake_case_   ,   snake_case_=1_2_3_4_5  ):
           _lowerCAmelCase       :  Optional[int]   				=					self.get_dummy_dataset()
           _lowerCAmelCase       :  str   				=					RagConfig(
               retrieval_vector_size=self.retrieval_vector_size   ,   question_encoder=DPRConfig().to_dict()   ,   generator=BartConfig().to_dict()   ,   index_name="""custom"""   ,   )
           if from_disk:
             _lowerCAmelCase       :  List[Any]   				=					os.path.join(self.tmpdirname   ,   """dataset"""  )
             _lowerCAmelCase       :  Dict   				=					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
             _lowerCAmelCase       :  Optional[Any]   				=					RagPyTorchDistributedRetriever(
                 snake_case_   ,   question_encoder_tokenizer=self.get_dpr_tokenizer()   ,   generator_tokenizer=self.get_bart_tokenizer()   ,   )
           else:
             _lowerCAmelCase       :  List[Any]   				=					RagPyTorchDistributedRetriever(
                 snake_case_   ,   question_encoder_tokenizer=self.get_dpr_tokenizer()   ,   generator_tokenizer=self.get_bart_tokenizer()   ,   index=CustomHFIndex(config.retrieval_vector_size   ,   snake_case_  )   ,   )
           if init_retrieval:
             retriever.init_retrieval(snake_case_  )
           return retriever
  
  
  
  
         def 							__UpperCamelCase       (     self   ,   snake_case_   ,   snake_case_  ):
           # Have to run in local mode because sys.path modifications at top of
           # file are not propogated to remote workers.
           # https://stackoverflow.com/questions/54338013/parallel-import-a-python-file-from-sibling-folder
           ray.init(local_mode=snake_case_  )
           _lowerCAmelCase       :  Optional[Any]   				=					self.get_dummy_dataset()
           _lowerCAmelCase       :  List[Any]   				=					RagConfig(
               retrieval_vector_size=self.retrieval_vector_size   ,   question_encoder=DPRConfig().to_dict()   ,   generator=BartConfig().to_dict()   ,   index_name="""custom"""   ,   )
           _lowerCAmelCase       :  List[Any]   				=					ray.remote(snake_case_  )
           _lowerCAmelCase       :  int   				=					[remote_cls.remote() for _ in range(1  )]
           if from_disk:
             _lowerCAmelCase       :  Tuple   				=					os.path.join(self.tmpdirname   ,   """dataset"""  )
             _lowerCAmelCase       :  Dict   				=					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
             _lowerCAmelCase       :  Dict   				=					RagRayDistributedRetriever(
                 snake_case_   ,   question_encoder_tokenizer=self.get_dpr_tokenizer()   ,   generator_tokenizer=self.get_bart_tokenizer()   ,   retrieval_workers=snake_case_   ,   index=CustomHFIndex.load_from_disk(
                     vector_size=config.retrieval_vector_size   ,   dataset_path=config.passages_path   ,   index_path=config.index_path   ,   )   ,   )
           else:
             _lowerCAmelCase       :  Dict   				=					RagRayDistributedRetriever(
                 snake_case_   ,   question_encoder_tokenizer=self.get_dpr_tokenizer()   ,   generator_tokenizer=self.get_bart_tokenizer()   ,   retrieval_workers=snake_case_   ,   index=CustomHFIndex(config.retrieval_vector_size   ,   snake_case_  )   ,   )
           if init_retrieval:
             retriever.init_retrieval()
           return retriever
  
  
  
  
         def 							__UpperCamelCase       (     self   ,   snake_case_   ,   snake_case_   ,   snake_case_  ):
           _lowerCAmelCase				,					_lowerCAmelCase				,					_lowerCAmelCase       :  List[str]   				=					retriever.retrieve(snake_case_   ,   n_docs=snake_case_  )
           self.assertEqual(retrieved_doc_embeds.shape   ,   (2, n_docs, self.retrieval_vector_size)  )
           self.assertEqual(len(snake_case_  )   ,   2  )
           self.assertEqual(sorted(doc_dicts[0]  )   ,   ["""embeddings""", """id""", """text""", """title"""]  )
           self.assertEqual(len(doc_dicts[0]["""id"""]  )   ,   snake_case_  )
           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  ):
           _lowerCAmelCase       :  Union[str, Any]   				=					1
           _lowerCAmelCase       :  int   				=					np.array(
               [np.ones(self.retrieval_vector_size  ), -np.ones(self.retrieval_vector_size  )]   ,   dtype=np.floataa  )
  
           self.distributed_retriever_check(
               self.get_dummy_pytorch_distributed_retriever(init_retrieval=snake_case_  )   ,   snake_case_   ,   snake_case_  )
  
  
  
  
         def 							__UpperCamelCase       (     self  ):
           _lowerCAmelCase       :  Optional[int]   				=					1
           _lowerCAmelCase       :  Tuple   				=					np.array(
               [np.ones(self.retrieval_vector_size  ), -np.ones(self.retrieval_vector_size  )]   ,   dtype=np.floataa  )
  
           self.distributed_retriever_check(
               self.get_dummy_custom_hf_index_pytorch_retriever(init_retrieval=snake_case_   ,   from_disk=snake_case_  )   ,   snake_case_   ,   snake_case_   ,   )
  
  
  
  
         def 							__UpperCamelCase       (     self  ):
           _lowerCAmelCase       :  str   				=					1
           _lowerCAmelCase       :  Dict   				=					np.array(
               [np.ones(self.retrieval_vector_size  ), -np.ones(self.retrieval_vector_size  )]   ,   dtype=np.floataa  )
  
           self.distributed_retriever_check(
               self.get_dummy_custom_hf_index_pytorch_retriever(init_retrieval=snake_case_   ,   from_disk=snake_case_  )   ,   snake_case_   ,   snake_case_   ,   )
  
  
  
  
         @require_ray
         def 							__UpperCamelCase       (     self  ):
           _lowerCAmelCase       :  Any   				=					1
           _lowerCAmelCase       :  Dict   				=					np.array(
               [np.ones(self.retrieval_vector_size  ), -np.ones(self.retrieval_vector_size  )]   ,   dtype=np.floataa  )
  
           self.distributed_retriever_check(
               self.get_dummy_ray_distributed_retriever(init_retrieval=snake_case_  )   ,   snake_case_   ,   snake_case_  )
           ray.shutdown()
  
  
  
  
         @require_ray
         def 							__UpperCamelCase       (     self  ):
           _lowerCAmelCase       :  str   				=					1
           _lowerCAmelCase       :  List[str]   				=					np.array(
               [np.ones(self.retrieval_vector_size  ), -np.ones(self.retrieval_vector_size  )]   ,   dtype=np.floataa  )
           with self.assertRaises(snake_case_  ):
             self.distributed_retriever_check(
                 self.get_dummy_custom_hf_index_ray_retriever(init_retrieval=snake_case_   ,   from_disk=snake_case_  )   ,   snake_case_   ,   snake_case_   ,   )
           ray.shutdown()
  
  
  
  
  
  
  
         @require_ray
         def 							__UpperCamelCase       (     self  ):
           _lowerCAmelCase       :  List[str]   				=					1
           _lowerCAmelCase       :  Dict   				=					np.array(
               [np.ones(self.retrieval_vector_size  ), -np.ones(self.retrieval_vector_size  )]   ,   dtype=np.floataa  )
  
           self.distributed_retriever_check(
               self.get_dummy_custom_hf_index_ray_retriever(init_retrieval=snake_case_   ,   from_disk=snake_case_  )   ,   snake_case_   ,   snake_case_  )
           ray.shutdown()
  
  
  
style_context: 
  '''simple docstring'''
  
  def 	_UpperCAmelCase				(  _lowerCamelCase						:       int  ,      _lowerCamelCase						:       int  ,      _lowerCamelCase						:       int		)    ->						float:
    if common_ratio == 1:
      # Formula for sum if common ratio is 1
      return num_of_terms * first_term
  
    # Formula for finding sum of n terms of a GeometricProgression
    return (first_term / (1 - common_ratio)) * (1 - common_ratio**num_of_terms)
  
  
  