






import logging

import numpy as np
import pytest
from scipy.linalg import eigh

logging.basicConfig(level=logging.INFO, format='%(message)s')

def      _lowerCamelCase	(						__A    :							np.ndarray )      ->					np.ndarray:
    return input_array.reshape((input_array.size, 1) )

def      _lowerCamelCase	(						__A    :							np.ndarray		,		__A    :							np.ndarray		,		__A    :							int )      ->					np.ndarray:
    _UpperCAmelCase				:      Any			  =				np.nan
    for i in range(__A ):
        _UpperCAmelCase				:      Union[str, Any]			  =				features[:, labels == i]
        _UpperCAmelCase				:      Any			  =				data.mean(1 )
        # Centralize the data of class i
        _UpperCAmelCase				:      List[Any]			  =				data - column_reshape(__A )
        if i > 0:
            # If covariance_sum is not None
            covariance_sum += np.dot(__A		,		centered_data.T )
        else:
            # If covariance_sum is np.nan (i.e. first loop)
            _UpperCAmelCase				:      Any			  =				np.dot(__A		,		centered_data.T )

    return covariance_sum / features.shape[1]

def      _lowerCamelCase	(						__A    :							np.ndarray		,		__A    :							np.ndarray		,		__A    :							int )      ->					np.ndarray:
    _UpperCAmelCase				:      Any			  =				features.mean(1 )
    _UpperCAmelCase				:      Optional[Any]			  =				np.nan
    for i in range(__A ):
        _UpperCAmelCase				:      Union[str, Any]			  =				features[:, labels == i]
        _UpperCAmelCase				:      int			  =				data.shape[1]
        _UpperCAmelCase				:      List[Any]			  =				data.mean(1 )
        if i > 0:
            # If covariance_sum is not None
            covariance_sum += device_data * np.dot(
                column_reshape(__A ) - column_reshape(__A )		,		(column_reshape(__A ) - column_reshape(__A )).T		,		)
        else:
            # If covariance_sum is np.nan (i.e. first loop)
            _UpperCAmelCase				:      Dict			  =				device_data * np.dot(
                column_reshape(__A ) - column_reshape(__A )		,		(column_reshape(__A ) - column_reshape(__A )).T		,		)

    return covariance_sum / features.shape[1]

def      _lowerCamelCase	(						__A    :							np.ndarray		,		__A    :							int )      ->					np.ndarray:

    # Check if the features have been loaded
    if features.any():
        _UpperCAmelCase				:      Any			  =				features.mean(1 )
        # Center the dataset
        _UpperCAmelCase				:      int			  =				features - np.reshape(__A		,		(data_mean.size, 1) )
        _UpperCAmelCase				:      int			  =				np.dot(__A		,		centered_data.T ) / features.shape[1]
        _UpperCAmelCase				:      Any			  =				np.linalg.eigh(__A )
        # Take all the columns in the reverse order (-1), and then takes only the first
        _UpperCAmelCase				:      List[Any]			  =				eigenvectors[:, ::-1][:, 0:dimensions]
        # Project the database on the new space
        _UpperCAmelCase				:      List[Any]			  =				np.dot(filtered_eigenvectors.T		,		__A )
        logging.info('''Principal Component Analysis computed''' )

        return projected_data
    else:
        logging.basicConfig(level=logging.ERROR		,		format='''%(message)s'''		,		force=__A )
        logging.error('''Dataset empty''' )
        raise AssertionError

def      _lowerCamelCase	(						__A    :							np.ndarray		,		__A    :							np.ndarray		,		__A    :							int		,		__A    :							int )      ->					np.ndarray:
    assert classes > dimensions

    # Check if features have been already loaded
    if features.any:
        _UpperCAmelCase				:      Optional[Any]			  =				eigh(
            covariance_between_classes(__A		,		__A		,		__A )		,		covariance_within_classes(__A		,		__A		,		__A )		,		)
        _UpperCAmelCase				:      Optional[int]			  =				eigenvectors[:, ::-1][:, :dimensions]
        _UpperCAmelCase				:      List[str]			  =				np.linalg.svd(__A )
        _UpperCAmelCase				:      Union[str, Any]			  =				svd_matrix[:, 0:dimensions]
        _UpperCAmelCase				:      Tuple			  =				np.dot(filtered_svd_matrix.T		,		__A )
        logging.info('''Linear Discriminant Analysis computed''' )

        return projected_data
    else:
        logging.basicConfig(level=logging.ERROR		,		format='''%(message)s'''		,		force=__A )
        logging.error('''Dataset empty''' )
        raise AssertionError

def      _lowerCamelCase	(						)      ->					None:
    # Create dummy dataset with 2 classes and 3 features
    _UpperCAmelCase				:      List[str]			  =				np.array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7]] )
    _UpperCAmelCase				:      Tuple			  =				np.array([0, 0, 0, 1, 1] )
    _UpperCAmelCase				:      Dict			  =				2
    _UpperCAmelCase				:      List[str]			  =				2

    # Assert that the function raises an AssertionError if dimensions > classes
    with pytest.raises(__A ) as error_info:
        _UpperCAmelCase				:      Dict			  =				linear_discriminant_analysis(
            __A		,		__A		,		__A		,		__A )
        if isinstance(__A		,		np.ndarray ):
            raise AssertionError(
                '''Did not raise AssertionError for dimensions > classes''' )
        assert error_info.type is AssertionError

def      _lowerCamelCase	(						)      ->					None:
    _UpperCAmelCase				:      List[str]			  =				np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]] )
    _UpperCAmelCase				:      List[str]			  =				2
    _UpperCAmelCase				:      str			  =				np.array([[6.92820323, 8.66025404, 10.39230485], [3.0, 3.0, 3.0]] )

    with pytest.raises(__A ) as error_info:
        _UpperCAmelCase				:      str			  =				principal_component_analysis(__A		,		__A )
        if not np.allclose(__A		,		__A ):
            raise AssertionError
        assert error_info.type is AssertionError


if __name__ == "__main__":
  import doctest

  doctest.testmod()












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

import datasets


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


SCREAMING_SNAKE_CASE 							=						'\\nThis metric is used to assess performance on the Mathematics Aptitude Test of Heuristics (MATH) dataset.\nIt first canonicalizes the inputs (e.g., converting "1/2" to "\\frac{1}{2}") and then computes accuracy.\n'


SCREAMING_SNAKE_CASE 							=						R'\nCalculates accuracy after canonicalizing inputs.\n\nArgs:\n    predictions: list of predictions to score. Each prediction\n        is a string that contains natural language and LaTex.\n    references: list of reference for each prediction. Each\n        reference is a string that contains natural language\n        and LaTex.\nReturns:\n    accuracy: accuracy after canonicalizing inputs\n        (e.g., converting "1/2" to "\\frac{1}{2}")\n\nExamples:\n    >>> metric = datasets.load_metric("competition_math")\n    >>> results = metric.compute(references=["\\frac{1}{2}"], predictions=["1/2"])\n    >>> print(results)\n    {\'accuracy\': 1.0}\n'
@datasets.utils.file_utils.add_end_docstrings(_DESCRIPTION ,   _KWARGS_DESCRIPTION			)
class 							A_    (						datasets.Metric			):






 '''simple docstring'''




 def  snake_case__				(	self) ->		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  snake_case__				(	self							,  _A							,  _A) ->		Tuple:

     """simple docstring"""



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




