





import logging

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

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

def     a_       (					lowerCAmelCase_ :     np.ndarray      ):
   return input_array.reshape((input_array.size, 1)      )

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

   return covariance_sum / features.shape[1]

def     a_       (					lowerCAmelCase_ :     np.ndarray,      lowerCAmelCase_ :     np.ndarray,      lowerCAmelCase_ :     int      ):
   __lowerCAmelCase				      =      features.mean(1      )
   __lowerCAmelCase				      =      np.nan
   for i in range(lowerCAmelCase_      ):
      __lowerCAmelCase				      =      features[:, labels == i]
      __lowerCAmelCase				      =      data.shape[1]
      __lowerCAmelCase				      =      data.mean(1      )
      if i > 0:
         # If covariance_sum is not None
         covariance_sum += device_data * np.dot(
             column_reshape(lowerCAmelCase_      ) - column_reshape(lowerCAmelCase_      ),      (column_reshape(lowerCAmelCase_      ) - column_reshape(lowerCAmelCase_      )).T,      )
      else:
         # If covariance_sum is np.nan (i.e. first loop)
         __lowerCAmelCase				      =      device_data * np.dot(
             column_reshape(lowerCAmelCase_      ) - column_reshape(lowerCAmelCase_      ),      (column_reshape(lowerCAmelCase_      ) - column_reshape(lowerCAmelCase_      )).T,      )

   return covariance_sum / features.shape[1]

def     a_       (					lowerCAmelCase_ :     np.ndarray,      lowerCAmelCase_ :     int      ):

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

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

def     a_       (					lowerCAmelCase_ :     np.ndarray,      lowerCAmelCase_ :     np.ndarray,      lowerCAmelCase_ :     int,      lowerCAmelCase_ :     int      ):
   assert classes > dimensions

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

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

def     a_       (					):
   # Create dummy dataset with 2 classes and 3 features
   __lowerCAmelCase				      =      np.array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7]]      )
   __lowerCAmelCase				      =      np.array([0, 0, 0, 1, 1]      )
   __lowerCAmelCase				      =      2
   __lowerCAmelCase				      =      2

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

def     a_       (					):
   __lowerCAmelCase				      =      np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]      )
   __lowerCAmelCase				      =      2
   __lowerCAmelCase				      =      np.array([[6.9282_0323, 8.6602_5404, 10.3923_0485], [3.0, 3.0, 3.0]]      )

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


if __name__ == "__main__":
     import doctest

     doctest.testmod()








UpperCAmelCase_							=				{"""a""": ["""c""", """b"""], """b""": ["""d""", """e"""], """c""": [], """d""": [], """e""": []}
UpperCAmelCase_							=				["""a""", """b""", """c""", """d""", """e"""]





def  __magic_name__  (				lowercase				,       lowercase				,       lowercase				)				-> Union[str, Any]:

							"""simple docstring"""



							lowercase_	:   Tuple  				=     start
							# add current to visited
							visited.append(lowercase				)
							lowercase_	:   Any  				=     edges[current]
							for neighbor in neighbors:
														# if neighbor not in visited, visit
														if neighbor not in visited:
																					lowercase_	:   List[str]  				=     topological_sort(lowercase				,       lowercase				,       lowercase				)
    # if all neighbors visited add current to sort
							sort.append(lowercase				)
							# if all vertices haven't been visited select a new one to visit
							if len(lowercase				) != len(lowercase				):
														for vertice in vertices:
																					if vertice not in visited:
																												lowercase_	:   Optional[Any]  				=     topological_sort(lowercase				,       lowercase				,       lowercase				)
    # return sort
							return sort


if __name__ == "__main__":
							UpperCAmelCase_							=				topological_sort("""a""", [], [])
							print(sort)