





"""simple docstring"""
import unittest

import numpy as np



def      __lowerCamelCase   (							a_     :		np.ndarray ,   a_     :		np.ndarray ,   a_     :		np.ndarray ,   a_     :		np.ndarray | None = None ,   )			->      np.ndarray:
      __SCREAMING_SNAKE_CASE   :List[str]						=  np.shape(_UpperCamelCase							)
      __SCREAMING_SNAKE_CASE   :Tuple						=  np.shape(_UpperCamelCase							)
      __SCREAMING_SNAKE_CASE   :Optional[int]						=  np.shape(_UpperCamelCase							)

      if shape_a[0] != shape_b[0]:
            __SCREAMING_SNAKE_CASE   :List[str]						=  (
                '''Expected the same number of rows for A and B. '''
                f'''Instead found A of size {shape_a} and B of size {shape_b}'''
            )
            raise ValueError(_UpperCamelCase							)

      if shape_b[1] != shape_c[1]:
            __SCREAMING_SNAKE_CASE   :List[str]						=  (
                '''Expected the same number of columns for B and C. '''
                f'''Instead found B of size {shape_b} and C of size {shape_c}'''
            )
            raise ValueError(_UpperCamelCase							)

      __SCREAMING_SNAKE_CASE   :List[str]						=  pseudo_inv
      if a_inv is None:
            try:
                  __SCREAMING_SNAKE_CASE   :List[Any]						=  np.linalg.inv(_UpperCamelCase							)
            except np.linalg.LinAlgError:
                  raise ValueError(
                      '''Input matrix A is not invertible. Cannot compute Schur complement.'''							)

      return mat_c - mat_b.T @ a_inv @ mat_b






class 					_SCREAMING_SNAKE_CASE(   unittest.TestCase  ):




       def     _UpperCamelCase     (						self							)			->      None:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE   :int						=  np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]							)
             __SCREAMING_SNAKE_CASE   :List[str]						=  np.array([[0, 3], [3, 0], [2, 3]]							)
             __SCREAMING_SNAKE_CASE   :Union[str, Any]						=  np.array([[2, 1], [6, 3]]							)

             __SCREAMING_SNAKE_CASE   :Optional[int]						=  schur_complement(_a		,_a		,_a							)

             __SCREAMING_SNAKE_CASE   :Optional[int]						=  np.block([[a, b], [b.T, c]]							)

             __SCREAMING_SNAKE_CASE   :Union[str, Any]						=  np.linalg.det(_a							)
             __SCREAMING_SNAKE_CASE   :Optional[Any]						=  np.linalg.det(_a							)
             __SCREAMING_SNAKE_CASE   :Union[str, Any]						=  np.linalg.det(_a							)

             self.assertAlmostEqual(_a		,det_a * det_s							)




       def     _UpperCamelCase     (						self							)			->      None:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE   :Optional[Any]						=  np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]							)
             __SCREAMING_SNAKE_CASE   :Optional[Any]						=  np.array([[0, 3], [3, 0], [2, 3]]							)
             __SCREAMING_SNAKE_CASE   :List[Any]						=  np.array([[2, 1], [6, 3]]							)

             with self.assertRaises(_a							):
                   schur_complement(_a		,_a		,_a							)




       def     _UpperCamelCase     (						self							)			->      None:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE   :int						=  np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]							)
             __SCREAMING_SNAKE_CASE   :Optional[Any]						=  np.array([[0, 3], [3, 0], [2, 3]]							)
             __SCREAMING_SNAKE_CASE   :Tuple						=  np.array([[2, 1, 3], [6, 3, 5]]							)

             with self.assertRaises(_a							):
                   schur_complement(_a		,_a		,_a							)


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  unittest.main()


'''simple docstring'''
import numpy as np
from nltk.translate import meteor_score

import datasets
from datasets.config import importlib_metadata, version


lowerCamelCase :      List[Any]					 =     version.parse(importlib_metadata.version("nltk"))
if NLTK_VERSION >= version.Version("3.6.4"):
     from nltk import word_tokenize


lowerCamelCase :      Any					 =     "\\n@inproceedings{banarjee2005,\n  title     = {{METEOR}: An Automatic Metric for {MT} Evaluation with Improved Correlation with Human Judgments},\n  author    = {Banerjee, Satanjeev  and Lavie, Alon},\n  booktitle = {Proceedings of the {ACL} Workshop on Intrinsic and Extrinsic Evaluation Measures for Machine Translation and/or Summarization},\n  month     = jun,\n  year      = {2005},\n  address   = {Ann Arbor, Michigan},\n  publisher = {Association for Computational Linguistics},\n  url       = {https://www.aclweb.org/anthology/W05-0909},\n  pages     = {65--72},\n}\n"

lowerCamelCase :      Optional[Any]					 =     "\\nMETEOR, an automatic metric for machine translation evaluation\nthat is based on a generalized concept of unigram matching between the\nmachine-produced translation and human-produced reference translations.\nUnigrams can be matched based on their surface forms, stemmed forms,\nand meanings; furthermore, METEOR can be easily extended to include more\nadvanced matching strategies. Once all generalized unigram matches\nbetween the two strings have been found, METEOR computes a score for\nthis matching using a combination of unigram-precision, unigram-recall, and\na measure of fragmentation that is designed to directly capture how\nwell-ordered the matched words in the machine translation are in relation\nto the reference.\n\nMETEOR gets an R correlation value of 0.347 with human evaluation on the Arabic\ndata and 0.331 on the Chinese data. This is shown to be an improvement on\nusing simply unigram-precision, unigram-recall and their harmonic F1\ncombination.\n"

lowerCamelCase :      Optional[Any]					 =     "\nComputes METEOR score of translated segments against one or more references.\nArgs:\n    predictions: list of predictions to score. Each prediction\n        should be a string with tokens separated by spaces.\n    references: list of reference for each prediction. Each\n        reference should be a string with tokens separated by spaces.\n    alpha: Parameter for controlling relative weights of precision and recall. default: 0.9\n    beta: Parameter for controlling shape of penalty as a function of fragmentation. default: 3\n    gamma: Relative weight assigned to fragmentation penalty. default: 0.5\nReturns:\n    'meteor': meteor score.\nExamples:\n\n    >>> meteor = datasets.load_metric('meteor')\n    >>> predictions = [\"It is a guide to action which ensures that the military always obeys the commands of the party\"]\n    >>> references = [\"It is a guide to action that ensures that the military will forever heed Party commands\"]\n    >>> results = meteor.compute(predictions=predictions, references=references)\n    >>> print(round(results[\"meteor\"], 4))\n    0.6944\n"







@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION     ,   _KWARGS_DESCRIPTION  )
class 							A__    (       datasets.Metric  ):





  def 						A  (		self      :	Tuple )	->    str:





       '''simple docstring'''






       return datasets.MetricInfo(
           description=_DESCRIPTION							,					citation=_CITATION							,					inputs_description=_KWARGS_DESCRIPTION							,					features=datasets.Features(
               {
                   'predictions': datasets.Value('string'							,					id='sequence' ),
                   'references': datasets.Value('string'							,					id='sequence' ),
               } )							,					codebase_urls=['https://github.com/nltk/nltk/blob/develop/nltk/translate/meteor_score.py']							,					reference_urls=[
               'https://www.nltk.org/api/nltk.translate.html#module-nltk.translate.meteor_score',
               'https://en.wikipedia.org/wiki/METEOR',
           ]							,					)





  def 						A  (		self      :	Union[str, Any]							,					_a      :	Union[str, Any] )	->    Optional[int]:





       '''simple docstring'''






       import nltk

       nltk.download('wordnet' )
       if NLTK_VERSION >= version.Version('3.6.5' ):
            nltk.download('punkt' )
       if NLTK_VERSION >= version.Version('3.6.6' ):
            nltk.download('omw-1.4' )





  def 						A  (		self      :	int							,					_a      :	Tuple							,					_a      :	List[str]							,					_a      :	List[str]=0.9							,					_a      :	Dict=3							,					_a      :	Optional[int]=0.5 )	->    Optional[int]:





       '''simple docstring'''






       if NLTK_VERSION >= version.Version('3.6.5' ):
            _SCREAMING_SNAKE_CASE							    =[
                meteor_score.single_meteor_score(
                    word_tokenize(_a )							,					word_tokenize(_a )							,					alpha=_a							,					beta=_a							,					gamma=_a )
                for ref, pred in zip(_a							,					_a )
            ]
       else:
            _SCREAMING_SNAKE_CASE							    =[
                meteor_score.single_meteor_score(_a							,					_a							,					alpha=_a							,					beta=_a							,					gamma=_a )
                for ref, pred in zip(_a							,					_a )
            ]

       return {"meteor": np.mean(_a )}
