





'''simple docstring'''




import mpmath  # for roots of unity
import numpy as np


class 					SCREAMING_SNAKE_CASE       :


     def __init__(		self		,      _UpperCAmelCase=None		,      _UpperCAmelCase=None):

          '''simple docstring'''






          __A		:					List[Any]						=			list(poly_a or [0])[:]
          __A		:					Optional[int]						=			list(poly_b or [0])[:]

          # Remove leading zero coefficients
          while self.polyA[-1] == 0:
               self.polyA.pop()
          __A		:					Union[str, Any]						=			len(self.polyA)

          while self.polyB[-1] == 0:
               self.polyB.pop()
          __A		:					Optional[int]						=			len(self.polyB)

          # Add 0 to make lengths equal a power of 2
          __A		:					Optional[Any]						=			int(
              2 ** np.ceil(np.loga(len(self.polyA) + len(self.polyB) - 1)))

          while len(self.polyA) < self.c_max_length:
               self.polyA.append(0)
          while len(self.polyB) < self.c_max_length:
               self.polyB.append(0)
          # A complex root used for the fourier transform
          __A		:					str						=			complex(mpmath.root(x=1		,      n=self.c_max_length		,      k=1))

          # The product
          __A		:					Tuple						=			self.__multiply()


     def 				SCREAMING_SNAKE_CASE    (		self		,      _UpperCAmelCase):

          '''simple docstring'''






          __A		:					Optional[int]						=			[[x] for x in self.polyA] if which == 'A' else [[x] for x in self.polyB]
          # Corner case
          if len(_UpperCAmelCase) <= 1:
               return dft[0]
          #
          __A		:					Dict						=			self.c_max_length // 2
          while next_ncol > 0:
               __A		:					Optional[Any]						=			[[] for i in range(_UpperCAmelCase)]
               __A		:					Tuple						=			self.root**next_ncol

               # First half of next step
               __A		:					Optional[Any]						=			1
               for j in range(self.c_max_length // (next_ncol * 2)):
                    for i in range(_UpperCAmelCase):
                         new_dft[i].append(dft[i][j] + current_root * dft[i + next_ncol][j])
                    current_root *= root
               # Second half of next step
               __A		:					List[str]						=			1
               for j in range(self.c_max_length // (next_ncol * 2)):
                    for i in range(_UpperCAmelCase):
                         new_dft[i].append(dft[i][j] - current_root * dft[i + next_ncol][j])
                    current_root *= root
               # Update
               __A		:					Optional[int]						=			new_dft
               __A		:					Tuple						=			next_ncol // 2
          return dft[0]


     def 				SCREAMING_SNAKE_CASE    (		self):

          '''simple docstring'''






          __A		:					int						=			self.__dft('A')
          __A		:					Optional[Any]						=			self.__dft('B')
          __A		:					str						=			[[dft_a[i] * dft_b[i] for i in range(self.c_max_length)]]
          del dft_a
          del dft_b

          # Corner Case
          if len(inverce_c[0]) <= 1:
               return inverce_c[0]
          # Inverse DFT
          __A		:					Dict						=			2
          while next_ncol <= self.c_max_length:
               __A		:					Optional[int]						=			[[] for i in range(_UpperCAmelCase)]
               __A		:					Any						=			self.root ** (next_ncol // 2)
               __A		:					Tuple						=			1
               # First half of next step
               for j in range(self.c_max_length // next_ncol):
                    for i in range(next_ncol // 2):
                         # Even positions
                         new_inverse_c[i].append(
                             (
                                 inverce_c[i][j]
                                 + inverce_c[i][j + self.c_max_length // next_ncol]
                             )
                             / 2)
                         # Odd positions
                         new_inverse_c[i + next_ncol // 2].append(
                             (
                                 inverce_c[i][j]
                                 - inverce_c[i][j + self.c_max_length // next_ncol]
                             )
                             / (2 * current_root))
                    current_root *= root
               # Update
               __A		:					int						=			new_inverse_c
               next_ncol *= 2
          # Unpack
          __A		:					Optional[int]						=			[round(x[0].real		,      8) + round(x[0].imag		,      8) * 1j for x in inverce_c]

          # Remove leading 0's
          while inverce_c[-1] == 0:
               inverce_c.pop()
          return inverce_c


     def __str__(		self):

          '''simple docstring'''






          __A		:					int						=			'A = ' + ' + '.join(
              F'{coef}*x^{i}' for coef, i in enumerate(self.polyA[: self.len_A]))
          __A		:					Optional[Any]						=			'B = ' + ' + '.join(
              F'{coef}*x^{i}' for coef, i in enumerate(self.polyB[: self.len_B]))
          __A		:					str						=			'A*B = ' + ' + '.join(
              F'{coef}*x^{i}' for coef, i in enumerate(self.product))

          return F'{a}\n{b}\n{c}'


# Unit tests
if __name__ == "__main__":
  import doctest

  doctest.testmod()


from jiwer import compute_measures

import datasets


A									=  '\\n@inproceedings{inproceedings,\n    author = {Morris, Andrew and Maier, Viktoria and Green, Phil},\n    year = {2004},\n    month = {01},\n    pages = {},\n    title = {From WER and RIL to MER and WIL: improved evaluation measures for connected speech recognition.}\n}\n'

A									=  '\\nWord error rate (WER) is a common metric of the performance of an automatic speech recognition system.\n\nThe general difficulty of measuring performance lies in the fact that the recognized word sequence can have a different length from the reference word sequence (supposedly the correct one). The WER is derived from the Levenshtein distance, working at the word level instead of the phoneme level. The WER is a valuable tool for comparing different systems as well as for evaluating improvements within one system. This kind of measurement, however, provides no details on the nature of translation errors and further work is therefore required to identify the main source(s) of error and to focus any research effort.\n\nThis problem is solved by first aligning the recognized word sequence with the reference (spoken) word sequence using dynamic string alignment. Examination of this issue is seen through a theory called the power law that states the correlation between perplexity and word error rate.\n\nWord error rate can then be computed as:\n\nWER = (S + D + I) / N = (S + D + I) / (S + D + C)\n\nwhere\n\nS is the number of substitutions,\nD is the number of deletions,\nI is the number of insertions,\nC is the number of correct words,\nN is the number of words in the reference (N=S+D+C).\n\nThis value indicates the average number of errors per reference word. The lower the value, the better the\nperformance of the ASR system with a WER of 0 being a perfect score.\n'

A									=  '\nCompute WER score of transcribed segments against references.\n\nArgs:\n    references: List of references for each speech input.\n    predictions: List of transcriptions to score.\n    concatenate_texts (bool, default=False): Whether to concatenate all input texts or compute WER iteratively.\n\nReturns:\n    (float): the word error rate\n\nExamples:\n\n    >>> predictions = ["this is the prediction", "there is an other sample"]\n    >>> references = ["this is the reference", "there is another one"]\n    >>> wer = datasets.load_metric("wer")\n    >>> wer_score = wer.compute(predictions=predictions, references=references)\n    >>> print(wer_score)\n    0.5\n'


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






			"""simple docstring"""




			def       __lowerCAmelCase			(     self				):

				"""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/jitsi/jiwer/']			,					reference_urls=[
				        'https://en.wikipedia.org/wiki/Word_error_rate',
				    ]			,					)







			def       __lowerCAmelCase			(     self			,					__UpperCamelCase=None			,					__UpperCamelCase=None			,					__UpperCamelCase=False				):

				"""simple docstring"""


				if concatenate_texts:
					return compute_measures(__UpperCamelCase			,					__UpperCamelCase				)["wer"]
				else:
					snake_case_   		=			0
					snake_case_   		=			0
					for prediction, reference in zip(__UpperCamelCase			,					__UpperCamelCase				):
						snake_case_   		=			compute_measures(__UpperCamelCase			,					__UpperCamelCase				)
						incorrect += measures["substitutions"] + measures["deletions"] + measures["insertions"]
						total += measures["substitutions"] + measures["deletions"] + measures["hits"]
					return incorrect / total
