



"""simple docstring"""
from __future__ import annotations



class    SCREAMING_SNAKE_CASE__						:

   def __init__(     self   ,  _SCREAMING_SNAKE_CASE		)						->   Union[str, Any]:





    '''simple docstring'''




    UpperCAmelCase			:      List[Any]			=			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(_SCREAMING_SNAKE_CASE		) != 0:
     UpperCAmelCase			:      Any			=			len(rows[0]		)
     if cols == 0:
      raise error
     for row in rows:
      if len(_SCREAMING_SNAKE_CASE		) != cols:
       raise error
      for value in row:
       if not isinstance(_SCREAMING_SNAKE_CASE   ,  (int, float)		):
        raise error
     UpperCAmelCase			:      Optional[int]			=			rows
    else:
     UpperCAmelCase			:      Tuple			=			[]

   def 			SCREAMING_SNAKE_CASE  (     self		)						->   list[list[int]]:





    '''simple docstring'''




    return [[row[i] for row in self.rows] for i in range(len(self.rows[0]		)		)]

   @property
   def 			SCREAMING_SNAKE_CASE  (     self		)						->   int:





    '''simple docstring'''




    return len(self.rows		)

   @property
   def 			SCREAMING_SNAKE_CASE  (     self		)						->   int:





    '''simple docstring'''




    return len(self.rows[0]		)

   @property
   def 			SCREAMING_SNAKE_CASE  (     self		)						->   tuple[int, int]:





    '''simple docstring'''




    return (self.num_rows, self.num_columns)

   @property
   def 			SCREAMING_SNAKE_CASE  (     self		)						->   bool:





    '''simple docstring'''




    return self.order[0] == self.order[1]

   def 			SCREAMING_SNAKE_CASE  (     self		)						->   Matrix:





    '''simple docstring'''




    UpperCAmelCase			:      str			=			[
        [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(_SCREAMING_SNAKE_CASE		)

   def 			SCREAMING_SNAKE_CASE  (     self		)						->   int:





    '''simple docstring'''




    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 			SCREAMING_SNAKE_CASE  (     self		)						->   bool:





    '''simple docstring'''




    return bool(self.determinant()		)

   def 			SCREAMING_SNAKE_CASE  (     self   ,  _SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE		)						->   int:





    '''simple docstring'''




    UpperCAmelCase			:      List[str]			=			[
        [
            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(_SCREAMING_SNAKE_CASE		).determinant()

   def 			SCREAMING_SNAKE_CASE  (     self   ,  _SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE		)						->   int:





    '''simple docstring'''




    if (row + column) % 2 == 0:
     return self.get_minor(_SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE		)
    return -1 * self.get_minor(_SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE		)

   def 			SCREAMING_SNAKE_CASE  (     self		)						->   Matrix:





    '''simple docstring'''




    return Matrix(
        [
            [self.get_minor(_SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE		) for column in range(self.num_columns		)]
            for row in range(self.num_rows		)
        ]		)

   def 			SCREAMING_SNAKE_CASE  (     self		)						->   Matrix:





    '''simple docstring'''




    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 			SCREAMING_SNAKE_CASE  (     self		)						->   Matrix:





    '''simple docstring'''




    UpperCAmelCase			:      Tuple			=			[
        [self.cofactors().rows[column][row] for column in range(self.num_columns		)]
        for row in range(self.num_rows		)
    ]
    return Matrix(_SCREAMING_SNAKE_CASE		)

   def 			SCREAMING_SNAKE_CASE  (     self		)						->   Matrix:





    '''simple docstring'''




    UpperCAmelCase			:      Any			=			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		)						->   str:





    '''simple docstring'''




    return str(self.rows		)

   def __str__(     self		)						->   str:





    '''simple docstring'''




    if self.num_rows == 0:
     return "[]"
    if self.num_rows == 1:
     return "[[" + ". ".join(str(self.rows[0]		)		) + "]]"
    return (
        "["
        + "\n ".join(
            [
                """[""" + """. """.join([str(_SCREAMING_SNAKE_CASE		) for value in row]		) + """.]"""
                for row in self.rows
            ]		)
        + "]"
    )

   def 			SCREAMING_SNAKE_CASE  (     self   ,  _SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE = None		)						->   None:





    '''simple docstring'''




    UpperCAmelCase			:      int			=			TypeError("""Row must be a list containing all ints and/or floats"""		)
    if not isinstance(_SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE		):
     raise type_error
    for value in row:
     if not isinstance(_SCREAMING_SNAKE_CASE   ,  (int, float)		):
      raise type_error
    if len(_SCREAMING_SNAKE_CASE		) != 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(_SCREAMING_SNAKE_CASE		)
    else:
     UpperCAmelCase			:      List[str]			=			self.rows[0:position] + [row] + self.rows[position:]

   def 			SCREAMING_SNAKE_CASE  (     self   ,  _SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE = None		)						->   None:





    '''simple docstring'''




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

   def __eq__(     self   ,  _SCREAMING_SNAKE_CASE		)						->   bool:





    '''simple docstring'''




    if not isinstance(_SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE		):
     return NotImplemented
    return self.rows == other.rows

   def __ne__(     self   ,  _SCREAMING_SNAKE_CASE		)						->   bool:





    '''simple docstring'''




    return not self == other

   def __neg__(     self		)						->   Matrix:





    '''simple docstring'''




    return self * -1

   def __add__(     self   ,  _SCREAMING_SNAKE_CASE		)						->   Matrix:





    '''simple docstring'''




    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   ,  _SCREAMING_SNAKE_CASE		)						->   Matrix:





    '''simple docstring'''




    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   ,  _SCREAMING_SNAKE_CASE		)						->   Matrix:





    '''simple docstring'''




    if isinstance(_SCREAMING_SNAKE_CASE   ,  (int, float)		):
     return Matrix(
         [[int(element * other		) for element in row] for row in self.rows]		)
    elif isinstance(_SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE		):
     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(_SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE		) 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   ,  _SCREAMING_SNAKE_CASE		)						->   Matrix:





    '''simple docstring'''




    if not isinstance(_SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE		):
     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			:      Optional[Any]			=			self
    for _ in range(other - 1		):
     result *= self
    return result




   @classmethod
   def 			SCREAMING_SNAKE_CASE  (     cls   ,  _SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE		)						->   int:





    '''simple docstring'''




    return sum(row[i] * column[i] for i in range(len(_SCREAMING_SNAKE_CASE		)		)		)


if __name__ == "__main__":
      import doctest

      doctest.testmod()





"""simple docstring"""
import datasets

from .nmt_bleu import compute_bleu  # From: https://github.com/tensorflow/nmt/blob/master/nmt/scripts/bleu.py


A:     Optional[Any]										=	"\\n@INPROCEEDINGS{Papineni02bleu:a,\n    author = {Kishore Papineni and Salim Roukos and Todd Ward and Wei-jing Zhu},\n    title = {BLEU: a Method for Automatic Evaluation of Machine Translation},\n    booktitle = {},\n    year = {2002},\n    pages = {311--318}\n}\n@inproceedings{lin-och-2004-orange,\n    title = \"{ORANGE}: a Method for Evaluating Automatic Evaluation Metrics for Machine Translation\",\n    author = \"Lin, Chin-Yew  and\n      Och, Franz Josef\",\n    booktitle = \"{COLING} 2004: Proceedings of the 20th International Conference on Computational Linguistics\",\n    month = \"aug 23{--}aug 27\",\n    year = \"2004\",\n    address = \"Geneva, Switzerland\",\n    publisher = \"COLING\",\n    url = \"https://www.aclweb.org/anthology/C04-1072\",\n    pages = \"501--507\",\n}\n"

A:     Optional[int]										=	"\\nBLEU (bilingual evaluation understudy) is an algorithm for evaluating the quality of text which has been machine-translated from one natural language to another.\nQuality is considered to be the correspondence between a machine's output and that of a human: \"the closer a machine translation is to a professional human translation,\nthe better it is\" – this is the central idea behind BLEU. BLEU was one of the first metrics to claim a high correlation with human judgements of quality, and\nremains one of the most popular automated and inexpensive metrics.\n\nScores are calculated for individual translated segments—generally sentences—by comparing them with a set of good quality reference translations.\nThose scores are then averaged over the whole corpus to reach an estimate of the translation's overall quality. Intelligibility or grammatical correctness\nare not taken into account[citation needed].\n\nBLEU's output is always a number between 0 and 1. This value indicates how similar the candidate text is to the reference texts, with values closer to 1\nrepresenting more similar texts. Few human translations will attain a score of 1, since this would indicate that the candidate is identical to one of the\nreference translations. For this reason, it is not necessary to attain a score of 1. Because there are more opportunities to match, adding additional\nreference translations will increase the BLEU score.\n"

A:     Optional[int]										=	"\nComputes BLEU score of translated segments against one or more references.\nArgs:\n    predictions: list of translations to score.\n        Each translation should be tokenized into a list of tokens.\n    references: list of lists of references for each translation.\n        Each reference should be tokenized into a list of tokens.\n    max_order: Maximum n-gram order to use when computing BLEU score.\n    smooth: Whether or not to apply Lin et al. 2004 smoothing.\nReturns:\n    'bleu': bleu score,\n    'precisions': geometric mean of n-gram precisions,\n    'brevity_penalty': brevity penalty,\n    'length_ratio': ratio of lengths,\n    'translation_length': translation_length,\n    'reference_length': reference_length\nExamples:\n\n    >>> predictions = [\n    ...     [\"hello\", \"there\", \"general\", \"kenobi\"],                             # tokenized prediction of the first sample\n    ...     [\"foo\", \"bar\", \"foobar\"]                                             # tokenized prediction of the second sample\n    ... ]\n    >>> references = [\n    ...     [[\"hello\", \"there\", \"general\", \"kenobi\"], [\"hello\", \"there\", \"!\"]],  # tokenized references for the first sample (2 references)\n    ...     [[\"foo\", \"bar\", \"foobar\"]]                                           # tokenized references for the second sample (1 reference)\n    ... ]\n    >>> bleu = datasets.load_metric(\"bleu\")\n    >>> results = bleu.compute(predictions=predictions, references=references)\n    >>> print(results[\"bleu\"])\n    1.0\n"



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

   def 			SCREAMING_SNAKE_CASE  (     self		)						->   Union[str, Any]:





    '''simple docstring'''




    return datasets.MetricInfo(
        description=_DESCRIPTION   ,  citation=_CITATION   ,  inputs_description=_KWARGS_DESCRIPTION   ,  features=datasets.Features(
            {
                """predictions""": datasets.Sequence(datasets.Value("""string"""   ,  id="""token"""		)   ,  id="""sequence"""		),
                """references""": datasets.Sequence(
                    datasets.Sequence(datasets.Value("""string"""   ,  id="""token"""		)   ,  id="""sequence"""		)   ,  id="""references"""		),
            }		)   ,  codebase_urls=["""https://github.com/tensorflow/nmt/blob/master/nmt/scripts/bleu.py"""]   ,  reference_urls=[
            """https://en.wikipedia.org/wiki/BLEU""",
            """https://towardsdatascience.com/evaluating-text-output-in-nlp-bleu-at-your-own-risk-e8609665a213""",
        ]   ,  )




   def 			SCREAMING_SNAKE_CASE  (     self   ,  _SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE=4   ,  _SCREAMING_SNAKE_CASE=False		)						->   Optional[int]:





    '''simple docstring'''




    UpperCAmelCase			:      Dict			=			compute_bleu(
        reference_corpus=_SCREAMING_SNAKE_CASE   ,  translation_corpus=_SCREAMING_SNAKE_CASE   ,  max_order=_SCREAMING_SNAKE_CASE   ,  smooth=_SCREAMING_SNAKE_CASE		)
    ((UpperCAmelCase)			,	(UpperCAmelCase)			,	(UpperCAmelCase)			,	(UpperCAmelCase)			,	(UpperCAmelCase)			,	(UpperCAmelCase))			:      Dict			=			score
    return {
        "bleu": bleu,
        "precisions": precisions,
        "brevity_penalty": bp,
        "length_ratio": ratio,
        "translation_length": translation_length,
        "reference_length": reference_length,
    }
