"""simple docstring"""







import logging

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

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



def     lowercase__( __SCREAMING_SNAKE_CASE							:  np.ndarray   ):
     return input_array.reshape((input_array.size, 1)   )



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

     return covariance_sum / features.shape[1]



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

     return covariance_sum / features.shape[1]



def     lowercase__( __SCREAMING_SNAKE_CASE							:  np.ndarray  ,    __SCREAMING_SNAKE_CASE							:  int   ):

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

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



def     lowercase__( __SCREAMING_SNAKE_CASE							:  np.ndarray  ,    __SCREAMING_SNAKE_CASE							:  np.ndarray  ,    __SCREAMING_SNAKE_CASE							:  int  ,    __SCREAMING_SNAKE_CASE							:  int   ):
     assert classes > dimensions

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

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



def     lowercase__( ):
     # Create dummy dataset with 2 classes and 3 features
     lowercase_			:       str									=			np.array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7]]   )
     lowercase_			:       List[str]									=			np.array([0, 0, 0, 1, 1]   )
     lowercase_			:       Any									=			2
     lowercase_			:       Any									=			2

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



def     lowercase__( ):
     lowercase_			:       List[str]									=			np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]   )
     lowercase_			:       List[str]									=			2
     lowercase_			:       Any									=			np.array([[6.9282_0323, 8.6602_5404, 10.3923_0485], [3.0, 3.0, 3.0]]   )

     with pytest.raises(__SCREAMING_SNAKE_CASE   ) as error_info:
          lowercase_			:       Union[str, Any]									=			principal_component_analysis(__SCREAMING_SNAKE_CASE  ,    __SCREAMING_SNAKE_CASE   )
          if not np.allclose(__SCREAMING_SNAKE_CASE  ,    __SCREAMING_SNAKE_CASE   ):
               raise AssertionError
          assert error_info.type is AssertionError


if __name__ == "__main__":
       import doctest

       doctest.testmod()


"""simple docstring"""







__SCREAMING_SNAKE_CASE								="ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/"



def     lowercase__( __SCREAMING_SNAKE_CASE							:  bytes   ):
     # Make sure the supplied data is a bytes-like object
     if not isinstance(__SCREAMING_SNAKE_CASE  ,    __SCREAMING_SNAKE_CASE   ):
          lowercase_			:       Dict									=			F'''a bytes-like object is required, not \'{data.__class__.__name__}\''''
          raise TypeError(__SCREAMING_SNAKE_CASE   )

     lowercase_			:       List[Any]									=			''.join(bin(__SCREAMING_SNAKE_CASE   )[2:].zfill(8   ) for byte in data   )

     lowercase_			:       List[Any]									=			len(__SCREAMING_SNAKE_CASE   ) % 6 != 0

     if padding_needed:
          # The padding that will be added later
          lowercase_			:       Optional[int]									=			b'=' * ((6 - len(__SCREAMING_SNAKE_CASE   ) % 6) // 2)

          # Append binary_stream with arbitrary binary digits (0's by default) to make its
          # length a multiple of 6.
          binary_stream += "0" * (6 - len(__SCREAMING_SNAKE_CASE   ) % 6)
     else:
          lowercase_			:       List[Any]									=			b''

     # Encode every 6 binary digits to their corresponding Base64 character
     return (
         "".join(
             B64_CHARSET[int(binary_stream[index : index + 6]  ,    2   )]
             for index in range(0  ,    len(__SCREAMING_SNAKE_CASE   )  ,    6   )   ).encode()
         + padding
     )



def     lowercase__( __SCREAMING_SNAKE_CASE							:  str   ):
     # Make sure encoded_data is either a string or a bytes-like object
     if not isinstance(__SCREAMING_SNAKE_CASE  ,    __SCREAMING_SNAKE_CASE   ) and not isinstance(__SCREAMING_SNAKE_CASE  ,    __SCREAMING_SNAKE_CASE   ):
          lowercase_			:       Tuple									=			(
              'argument should be a bytes-like object or ASCII string, '
              F'''not \'{encoded_data.__class__.__name__}\''''
          )
          raise TypeError(__SCREAMING_SNAKE_CASE   )

     # In case encoded_data is a bytes-like object, make sure it contains only
     # ASCII characters so we convert it to a string object
     if isinstance(__SCREAMING_SNAKE_CASE  ,    __SCREAMING_SNAKE_CASE   ):
          try:
               lowercase_			:       List[str]									=			encoded_data.decode('utf-8'   )
          except UnicodeDecodeError:
               raise ValueError('base64 encoded data should only contain ASCII characters'   )

     lowercase_			:       List[str]									=			encoded_data.count('='   )

     # Check if the encoded string contains non base64 characters
     if padding:
          assert all(
              char in B64_CHARSET for char in encoded_data[:-padding]   ), "Invalid base64 character(s) found."
     else:
          assert all(
              char in B64_CHARSET for char in encoded_data   ), "Invalid base64 character(s) found."

     # Check the padding
     assert len(__SCREAMING_SNAKE_CASE   ) % 4 == 0 and padding < 3, "Incorrect padding"

     if padding:
          # Remove padding if there is one
          lowercase_			:       Union[str, Any]									=			encoded_data[:-padding]

          lowercase_			:       List[Any]									=			''.join(
              bin(B64_CHARSET.index(__SCREAMING_SNAKE_CASE   )   )[2:].zfill(6   ) for char in encoded_data   )[: -padding * 2]
     else:
          lowercase_			:       int									=			''.join(
              bin(B64_CHARSET.index(__SCREAMING_SNAKE_CASE   )   )[2:].zfill(6   ) for char in encoded_data   )

     lowercase_			:       str									=			[
         int(binary_stream[index : index + 8]  ,    2   )
         for index in range(0  ,    len(__SCREAMING_SNAKE_CASE   )  ,    8   )
     ]

     return bytes(__SCREAMING_SNAKE_CASE   )


if __name__ == "__main__":
       import doctest

       doctest.testmod()

