


from scipy.stats import pearsonr

import datasets


SCREAMING_SNAKE_CASE       :		Dict         =				"\nPearson correlation coefficient and p-value for testing non-correlation.\nThe Pearson correlation coefficient measures the linear relationship between two datasets. The calculation of the p-value relies on the assumption that each dataset is normally distributed. Like other correlation coefficients, this one varies between -1 and +1 with 0 implying no correlation. Correlations of -1 or +1 imply an exact linear relationship. Positive correlations imply that as x increases, so does y. Negative correlations imply that as x increases, y decreases.\nThe p-value roughly indicates the probability of an uncorrelated system producing datasets that have a Pearson correlation at least as extreme as the one computed from these datasets.\n"


SCREAMING_SNAKE_CASE       :		str         =				"\nArgs:\n    predictions (`list` of `int`): Predicted class labels, as returned by a model.\n    references (`list` of `int`): Ground truth labels.\n    return_pvalue (`boolean`): If `True`, returns the p-value, along with the correlation coefficient. If `False`, returns only the correlation coefficient. Defaults to `False`.\n\nReturns:\n    pearsonr (`float`): Pearson correlation coefficient. Minimum possible value is -1. Maximum possible value is 1. Values of 1 and -1 indicate exact linear positive and negative relationships, respectively. A value of 0 implies no correlation.\n    p-value (`float`): P-value, which roughly indicates the probability of an The p-value roughly indicates the probability of an uncorrelated system producing datasets that have a Pearson correlation at least as extreme as the one computed from these datasets. Minimum possible value is 0. Maximum possible value is 1. Higher values indicate higher probabilities.\n\nExamples:\n\n    Example 1-A simple example using only predictions and references.\n        >>> pearsonr_metric = datasets.load_metric(\"pearsonr\")\n        >>> results = pearsonr_metric.compute(predictions=[10, 9, 2.5, 6, 4], references=[1, 2, 3, 4, 5])\n        >>> print(round(results['pearsonr'], 2))\n        -0.74\n\n    Example 2-The same as Example 1, but that also returns the `p-value`.\n        >>> pearsonr_metric = datasets.load_metric(\"pearsonr\")\n        >>> results = pearsonr_metric.compute(predictions=[10, 9, 2.5, 6, 4], references=[1, 2, 3, 4, 5], return_pvalue=True)\n        >>> print(sorted(list(results.keys())))\n        ['p-value', 'pearsonr']\n        >>> print(round(results['pearsonr'], 2))\n        -0.74\n        >>> print(round(results['p-value'], 2))\n        0.15\n"


SCREAMING_SNAKE_CASE       :		Any         =				"\n@article{2020SciPy-NMeth,\nauthor  = {Virtanen, Pauli and Gommers, Ralf and Oliphant, Travis E. and\n      Haberland, Matt and Reddy, Tyler and Cournapeau, David and\n      Burovski, Evgeni and Peterson, Pearu and Weckesser, Warren and\n      Bright, Jonathan and {van der Walt}, St{\'e}fan J. and\n      Brett, Matthew and Wilson, Joshua and Millman, K. Jarrod and\n      Mayorov, Nikolay and Nelson, Andrew R. J. and Jones, Eric and\n      Kern, Robert and Larson, Eric and Carey, C J and\n      Polat, Ilhan and Feng, Yu and Moore, Eric W. and\n      {VanderPlas}, Jake and Laxalde, Denis and Perktold, Josef and\n      Cimrman, Robert and Henriksen, Ian and Quintero, E. A. and\n      Harris, Charles R. and Archibald, Anne M. and\n      Ribeiro, Antonio H. and Pedregosa, Fabian and\n      {van Mulbregt}, Paul and {SciPy 1.0 Contributors}},\ntitle   = {{{SciPy} 1.0: Fundamental Algorithms for Scientific\n      Computing in Python}},\njournal = {Nature Methods},\nyear    = {2020},\nvolume  = {17},\npages   = {261--272},\nadsurl  = {https://rdcu.be/b08Wh},\ndoi = {10.1038/s41592-019-0686-2},\n}\n"






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


   '''simple docstring'''







   def 		UpperCamelCase  (     self		):
        return datasets.MetricInfo(
            description=_DESCRIPTION   ,							citation=_CITATION   ,							inputs_description=_KWARGS_DESCRIPTION   ,							features=datasets.Features(
                {
                    '''predictions''': datasets.Value('''float'''		),
                    '''references''': datasets.Value('''float'''		),
                }		)   ,							reference_urls=['''https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.pearsonr.html''']   ,							)




   def 		UpperCamelCase  (     self   ,							UpperCamelCase_   ,							UpperCamelCase_   ,							UpperCamelCase_=False		):
        if return_pvalue:
             lowercase_       :str     =       pearsonr(UpperCamelCase_   ,							UpperCamelCase_		)
             return {"pearsonr": results[0], "p-value": results[1]}
        else:
             return {"pearsonr": float(pearsonr(UpperCamelCase_   ,							UpperCamelCase_		)[0]		)}





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




def     UpperCamelCase    (      _a		)					->							float:
     '''simple docstring'''





     return np.dot(_a       ,		_a		)






class      UpperCamelCase					:


   '''simple docstring'''







   def __init__(     self   ,							*,
       UpperCamelCase_ = np.inf   ,							UpperCamelCase_ = "linear"   ,							UpperCamelCase_ = 0.0   ,							):
        lowercase_       :Dict     =       regularization
        lowercase_       :Optional[Any]     =       gamma
        if kernel == "linear":
             lowercase_       :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'''		)
             lowercase_       :Union[str, 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:
             lowercase_       :str     =       f"Unknown kernel: {kernel}"
             raise ValueError(UpperCamelCase_		)
   def 		UpperCamelCase  (     self   ,							UpperCamelCase_   ,							UpperCamelCase_		):
        return np.dot(UpperCamelCase_   ,							UpperCamelCase_		)
   def 		UpperCamelCase  (     self   ,							UpperCamelCase_   ,							UpperCamelCase_		):
        return np.exp(-(self.gamma * norm_squared(vectora - vectora		))		)
   def 		UpperCamelCase  (     self   ,							UpperCamelCase_   ,							UpperCamelCase_		):
        lowercase_       :Tuple     =       observations
        lowercase_       :Union[str, Any]     =       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

        ((lowercase_)    ,      )       :Optional[Any]     =       np.shape(UpperCamelCase_		)

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

        lowercase_       :Dict     =       LinearConstraint(UpperCamelCase_   ,							0   ,							0		)
        lowercase_       :Optional[Any]     =       Bounds(0   ,							self.regularization		)

        lowercase_       :Any     =       minimize(
            UpperCamelCase_   ,							np.ones(UpperCamelCase_		)   ,							bounds=UpperCamelCase_   ,							constraints=[ly_contraint]		).x
        lowercase_       :Tuple     =       l_star

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




   def 		UpperCamelCase  (     self   ,							UpperCamelCase_		):
        lowercase_       :Union[str, Any]     =       sum(
            self.optimum[n]
            * self.classes[n]
            * self.kernel(self.observations[n]   ,							UpperCamelCase_		)
            for n in range(len(self.classes		)		)		)
        return 1 if s + self.offset >= 0 else -1


if __name__ == "__main__":
   import doctest

   doctest.testmod()

