
import numpy as np
from numpy import ndarray
from scipy.optimize import Bounds, LinearConstraint, minimize


def      UpperCamelCase   (       __lowerCamelCase	:					ndarray       ):
       return np.dot(__lowerCamelCase							,   __lowerCamelCase       )






class     UpperCAmelCase						:



   def __init__(self						:   Any       ,		*,
       snake_case__						:   float = np.inf       ,		snake_case__						:   str = "linear"       ,		snake_case__						:   float = 0.0       ,		)						->      None:


          '''simple docstring'''


          snake_case			:  Optional[int]     							= regularization
          snake_case			:  Optional[Any]     							= gamma
          if kernel == "linear":
                 snake_case			:  Optional[Any]     							= self.__linear
          elif kernel == "rbf":
                 if self.gamma == 0:
                        raise ValueError("rbf kernel requires gamma"					)
                 if not isinstance(self.gamma       ,		(float, int)					):
                        raise ValueError("gamma must be float or int"					)
                 if not self.gamma > 0:
                        raise ValueError("gamma must be > 0"					)
                 snake_case			:  Any     							= self.__rbf
                 # in the future, there could be a default value like in sklearn
                 # sklear: def_gamma = 1/(n_features * X.var()) (wiki)
                 # previously it was 1/(n_features)
          else:
                 snake_case			:  List[str]     							= f"""Unknown kernel: {kernel}"""
                 raise ValueError(snake_case__					)



   def 							_SCREAMING_SNAKE_CASE  (self						:   Union[str, Any]       ,		snake_case__						:   ndarray       ,		snake_case__						:   ndarray					)						->      float:


          '''simple docstring'''


          return np.dot(snake_case__       ,		snake_case__					)



   def 							_SCREAMING_SNAKE_CASE  (self						:   Union[str, Any]       ,		snake_case__						:   ndarray       ,		snake_case__						:   ndarray					)						->      float:


          '''simple docstring'''


          return np.exp(-(self.gamma * norm_squared(vectora - vectora					))					)



   def 							_SCREAMING_SNAKE_CASE  (self						:   List[Any]       ,		snake_case__						:   list[ndarray]       ,		snake_case__						:   ndarray					)						->      None:


          '''simple docstring'''


          snake_case			:  Tuple     							= observations
          snake_case			:  Dict     							= classes

          # using Wolfe's Dual to calculate w.
          # Primal problem: minimize 1/2*norm_squared(w)
          #   constraint: yn(w . xn + b) >= 1
          #
          # With l a vector
          # Dual problem: maximize sum_n(ln) -
          #       1/2 * sum_n(sum_m(ln*lm*yn*ym*xn . xm))
          #   constraint: self.C >= ln >= 0
          #           and sum_n(ln*yn) = 0
          # Then we get w using w = sum_n(ln*yn*xn)
          # At the end we can get b ~= mean(yn - w . xn)
          #
          # Since we use kernels, we only need l_star to calculate b
          # and to classify observations

          ((snake_case)							,   )			:  Optional[int]     							= np.shape(snake_case__					)

          def to_minimize(snake_case__						:   ndarray					) -> float:
                 snake_case			:  Dict     							= 0
                 ((snake_case)							,   )			:  Tuple     							= np.shape(snake_case__					)
                 for i in range(snake_case__					):
                        for j in range(snake_case__					):
                               s += (
                                   candidate[i]
                                   * candidate[j]
                                   * classes[i]
                                   * classes[j]
                                   * self.kernel(observations[i]       ,		observations[j]					)
                               )
                 return 1 / 2 * s - sum(snake_case__					)

          snake_case			:  Any     							= LinearConstraint(snake_case__       ,		0       ,		0					)
          snake_case			:  Optional[int]     							= Bounds(0       ,		self.regularization					)

          snake_case			:  List[str]     							= minimize(
              snake_case__       ,		np.ones(snake_case__					)       ,		bounds=snake_case__       ,		constraints=[ly_contraint]					).x
          snake_case			:  str     							= l_star

          # calculating mean offset of separation plane to points
          snake_case			:  List[str]     							= 0
          for i in range(snake_case__					):
                 for j in range(snake_case__					):
                        s += classes[i] - classes[i] * self.optimum[i] * self.kernel(
                            observations[i]       ,		observations[j]					)
          snake_case			:  Optional[Any]     							= s / n



   def 							_SCREAMING_SNAKE_CASE  (self						:   str       ,		snake_case__						:   ndarray					)						->      int:


          '''simple docstring'''


          snake_case			:  Tuple     							= sum(
              self.optimum[n]
              * self.classes[n]
              * self.kernel(self.observations[n]       ,		snake_case__					)
              for n in range(len(self.classes					)					)					)
          return 1 if s + self.offset >= 0 else -1


if __name__ == "__main__":
   import doctest

   doctest.testmod()







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

import datasets


__lowerCamelCase				=			"""\
@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}
}
"""


__lowerCamelCase				=			"""\
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.
"""


__lowerCamelCase				=			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     UpperCAmelCase						(		datasets.Metric					):



   def 							_SCREAMING_SNAKE_CASE  (self						:   Optional[int]					)						->      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 							_SCREAMING_SNAKE_CASE  (self						:   Optional[int]       ,		snake_case__						:   str       ,		snake_case__						:   List[Any]					)						->      Optional[Any]:


          '''simple docstring'''


          snake_case			:  Optional[int]     							= 0.0
          for i, j in zip(snake_case__       ,		snake_case__					):
                 n_correct += 1.0 if math_equivalence.is_equiv(snake_case__       ,		snake_case__					) else 0.0
          snake_case			:  Optional[int]     							= n_correct / len(snake_case__					)
          return {
              "accuracy": accuracy,
          }





