





from math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter




def     a__ (					lowercase__  ,    lowercase__  ,    lowercase__ = 1 / sqrt(2  )  ):






   '''simple docstring'''






   UpperCAmelCase_											=tau * frequency / samplerate
   UpperCAmelCase_											=sin(lowercase__  )
   UpperCAmelCase_											=cos(lowercase__  )
   UpperCAmelCase_											=_sin / (2 * q_factor)

   UpperCAmelCase_											=(1 - _cos) / 2
   UpperCAmelCase_											=1 - _cos

   UpperCAmelCase_											=1 + alpha
   UpperCAmelCase_											=-2 * _cos
   UpperCAmelCase_											=1 - alpha

   UpperCAmelCase_											=IIRFilter(2  )
   filt.set_coefficients([aa, aa, aa]  ,    [ba, ba, ba]  )
   return filt




def     a__ (					lowercase__  ,    lowercase__  ,    lowercase__ = 1 / sqrt(2  )  ):






   '''simple docstring'''






   UpperCAmelCase_											=tau * frequency / samplerate
   UpperCAmelCase_											=sin(lowercase__  )
   UpperCAmelCase_											=cos(lowercase__  )
   UpperCAmelCase_											=_sin / (2 * q_factor)

   UpperCAmelCase_											=(1 + _cos) / 2
   UpperCAmelCase_											=-1 - _cos

   UpperCAmelCase_											=1 + alpha
   UpperCAmelCase_											=-2 * _cos
   UpperCAmelCase_											=1 - alpha

   UpperCAmelCase_											=IIRFilter(2  )
   filt.set_coefficients([aa, aa, aa]  ,    [ba, ba, ba]  )
   return filt




def     a__ (					lowercase__  ,    lowercase__  ,    lowercase__ = 1 / sqrt(2  )  ):






   '''simple docstring'''






   UpperCAmelCase_											=tau * frequency / samplerate
   UpperCAmelCase_											=sin(lowercase__  )
   UpperCAmelCase_											=cos(lowercase__  )
   UpperCAmelCase_											=_sin / (2 * q_factor)

   UpperCAmelCase_											=_sin / 2
   UpperCAmelCase_											=0
   UpperCAmelCase_											=-ba

   UpperCAmelCase_											=1 + alpha
   UpperCAmelCase_											=-2 * _cos
   UpperCAmelCase_											=1 - alpha

   UpperCAmelCase_											=IIRFilter(2  )
   filt.set_coefficients([aa, aa, aa]  ,    [ba, ba, ba]  )
   return filt




def     a__ (					lowercase__  ,    lowercase__  ,    lowercase__ = 1 / sqrt(2  )  ):






   '''simple docstring'''






   UpperCAmelCase_											=tau * frequency / samplerate
   UpperCAmelCase_											=sin(lowercase__  )
   UpperCAmelCase_											=cos(lowercase__  )
   UpperCAmelCase_											=_sin / (2 * q_factor)

   UpperCAmelCase_											=1 - alpha
   UpperCAmelCase_											=-2 * _cos
   UpperCAmelCase_											=1 + alpha

   UpperCAmelCase_											=IIRFilter(2  )
   filt.set_coefficients([ba, ba, ba]  ,    [ba, ba, ba]  )
   return filt




def     a__ (					lowercase__  ,    lowercase__  ,    lowercase__  ,    lowercase__ = 1 / sqrt(2  )  ,    ):






   '''simple docstring'''






   UpperCAmelCase_											=tau * frequency / samplerate
   UpperCAmelCase_											=sin(lowercase__  )
   UpperCAmelCase_											=cos(lowercase__  )
   UpperCAmelCase_											=_sin / (2 * q_factor)
   UpperCAmelCase_											=1_0 ** (gain_db / 4_0)

   UpperCAmelCase_											=1 + alpha * big_a
   UpperCAmelCase_											=-2 * _cos
   UpperCAmelCase_											=1 - alpha * big_a
   UpperCAmelCase_											=1 + alpha / big_a
   UpperCAmelCase_											=-2 * _cos
   UpperCAmelCase_											=1 - alpha / big_a

   UpperCAmelCase_											=IIRFilter(2  )
   filt.set_coefficients([aa, aa, aa]  ,    [ba, ba, ba]  )
   return filt




def     a__ (					lowercase__  ,    lowercase__  ,    lowercase__  ,    lowercase__ = 1 / sqrt(2  )  ,    ):






   '''simple docstring'''






   UpperCAmelCase_											=tau * frequency / samplerate
   UpperCAmelCase_											=sin(lowercase__  )
   UpperCAmelCase_											=cos(lowercase__  )
   UpperCAmelCase_											=_sin / (2 * q_factor)
   UpperCAmelCase_											=1_0 ** (gain_db / 4_0)
   UpperCAmelCase_											=(big_a + 1) - (big_a - 1) * _cos
   UpperCAmelCase_											=(big_a + 1) + (big_a - 1) * _cos
   UpperCAmelCase_											=(big_a - 1) - (big_a + 1) * _cos
   UpperCAmelCase_											=(big_a - 1) + (big_a + 1) * _cos
   UpperCAmelCase_											=2 * sqrt(lowercase__  ) * alpha

   UpperCAmelCase_											=big_a * (pmc + aaa)
   UpperCAmelCase_											=2 * big_a * mpc
   UpperCAmelCase_											=big_a * (pmc - aaa)
   UpperCAmelCase_											=ppmc + aaa
   UpperCAmelCase_											=-2 * pmpc
   UpperCAmelCase_											=ppmc - aaa

   UpperCAmelCase_											=IIRFilter(2  )
   filt.set_coefficients([aa, aa, aa]  ,    [ba, ba, ba]  )
   return filt





def     a__ (					lowercase__  ,    lowercase__  ,    lowercase__  ,    lowercase__ = 1 / sqrt(2  )  ,    ):






   '''simple docstring'''






   UpperCAmelCase_											=tau * frequency / samplerate
   UpperCAmelCase_											=sin(lowercase__  )
   UpperCAmelCase_											=cos(lowercase__  )
   UpperCAmelCase_											=_sin / (2 * q_factor)
   UpperCAmelCase_											=1_0 ** (gain_db / 4_0)
   UpperCAmelCase_											=(big_a + 1) - (big_a - 1) * _cos
   UpperCAmelCase_											=(big_a + 1) + (big_a - 1) * _cos
   UpperCAmelCase_											=(big_a - 1) - (big_a + 1) * _cos
   UpperCAmelCase_											=(big_a - 1) + (big_a + 1) * _cos
   UpperCAmelCase_											=2 * sqrt(lowercase__  ) * alpha

   UpperCAmelCase_											=big_a * (ppmc + aaa)
   UpperCAmelCase_											=-2 * big_a * pmpc
   UpperCAmelCase_											=big_a * (ppmc - aaa)
   UpperCAmelCase_											=pmc + aaa
   UpperCAmelCase_											=2 * mpc
   UpperCAmelCase_											=pmc - aaa

   UpperCAmelCase_											=IIRFilter(2  )
   filt.set_coefficients([aa, aa, aa]  ,    [ba, ba, ba]  )
   return filt











import math_equivalence  # From: git+https://github.com/hendrycks/math.git

import datasets


__lowercase  :   int						      ="""\
@article{hendrycksmath2021,
  title={Measuring Mathematical Problem Solving With the MATH Dataset},
  author={Dan Hendrycks
    and Collin Burns
    and Saurav Kadavath
    and Akul Arora
    and Steven Basart
    and Eric Tang
    and Dawn Song
    and Jacob Steinhardt},
  journal={arXiv preprint arXiv:2103.03874},
  year={2021}
}
"""


__lowercase  :   List[Any]						      ="""\
This metric is used to assess performance on the Mathematics Aptitude Test of Heuristics (MATH) dataset.
It first canonicalizes the inputs (e.g., converting \"1/2\" to \"\\frac{1}{2}\") and then computes accuracy.
"""


__lowercase  :   str						      =R"""
Calculates accuracy after canonicalizing inputs.

Args:
    predictions: list of predictions to score. Each prediction
        is a string that contains natural language and LaTex.
    references: list of reference for each prediction. Each
        reference is a string that contains natural language
        and LaTex.
Returns:
    accuracy: accuracy after canonicalizing inputs
        (e.g., converting \"1/2\" to \"\\frac{1}{2}\")

Examples:
    >>> metric = datasets.load_metric(\"competition_math\")
    >>> results = metric.compute(references=[\"\\frac{1}{2}\"], predictions=[\"1/2\"])
    >>> print(results)
    {'accuracy': 1.0}
"""

@datasets.utils.file_utils.add_end_docstrings(_DESCRIPTION		,      _KWARGS_DESCRIPTION						)
class      A       (	datasets.Metric						):



      def 	lowerCAmelCase__    (	self:						Any       )						->    Optional[Any]:
         '''simple docstring'''

         return datasets.MetricInfo(
             description=_DESCRIPTION		,  citation=_CITATION		,  inputs_description=_KWARGS_DESCRIPTION		,  features=datasets.Features(
                 {
                     "predictions": datasets.Value("string"       ),
                     "references": datasets.Value("string"       ),
                 }       )		,  homepage="https://github.com/hendrycks/math"		,  codebase_urls=["https://github.com/hendrycks/math"]		,  )






      def 	lowerCAmelCase__    (	self:						Any		,  _lowerCAmelCase:						Tuple		,  _lowerCAmelCase:						Union[str, Any]       )						->    Dict:
         '''simple docstring'''

         UpperCAmelCase_											=0.0
         for i, j in zip(_lowerCAmelCase		,  _lowerCAmelCase       ):
            n_correct += 1.0 if math_equivalence.is_equiv(_lowerCAmelCase		,  _lowerCAmelCase       ) else 0.0
         UpperCAmelCase_											=n_correct / len(_lowerCAmelCase       )
         return {
             "accuracy": accuracy,
         }




