





import logging

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

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





def       _UpperCamelCase       (a__				:np.ndarray    ):






				"""simple docstring"""





				return input_array.reshape((input_array.size, 1)    )





def       _UpperCamelCase       (a__				:np.ndarray				,     a__				:np.ndarray				,     a__				:int    ):






				"""simple docstring"""





				UpperCamelCase__			       =     np.nan
				for i in range(a__    ):
								UpperCamelCase__			       =     features[:, labels == i]
								UpperCamelCase__			       =     data.mean(1    )
								# Centralize the data of class i
								UpperCamelCase__			       =     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__			       =     np.dot(a__				,     centered_data.T    )

				return covariance_sum / features.shape[1]





def       _UpperCamelCase       (a__				:np.ndarray				,     a__				:np.ndarray				,     a__				:int    ):






				"""simple docstring"""





				UpperCamelCase__			       =     features.mean(1    )
				UpperCamelCase__			       =     np.nan
				for i in range(a__    ):
								UpperCamelCase__			       =     features[:, labels == i]
								UpperCamelCase__			       =     data.shape[1]
								UpperCamelCase__			       =     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__			       =     device_data * np.dot(
												    column_reshape(a__    ) - column_reshape(a__    )				,     (column_reshape(a__    ) - column_reshape(a__    )).T				,     )

				return covariance_sum / features.shape[1]





def       _UpperCamelCase       (a__				:np.ndarray				,     a__				:int    ):






				"""simple docstring"""





				if features.any():
								UpperCamelCase__			       =     features.mean(1    )
								# Center the dataset
								UpperCamelCase__			       =     features - np.reshape(a__				,     (data_mean.size, 1)    )
								UpperCamelCase__			       =     np.dot(a__				,     centered_data.T    ) / features.shape[1]
								UpperCamelCase__       ,       UpperCamelCase__			       =     np.linalg.eigh(a__    )
								# Take all the columns in the reverse order (-1), and then takes only the first
								UpperCamelCase__			       =     eigenvectors[:, ::-1][:, 0:dimensions]
								# Project the database on the new space
								UpperCamelCase__			       =     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       _UpperCamelCase       (a__				:np.ndarray				,     a__				:np.ndarray				,     a__				:int				,     a__				:int    ):






				"""simple docstring"""





				assert classes > dimensions

				# Check if features have been already loaded
				if features.any:
								UpperCamelCase__       ,       UpperCamelCase__			       =     eigh(
								    covariance_between_classes(a__				,     a__				,     a__    )				,     covariance_within_classes(a__				,     a__				,     a__    )				,     )
								UpperCamelCase__			       =     eigenvectors[:, ::-1][:, :dimensions]
								UpperCamelCase__       ,       UpperCamelCase__       ,       UpperCamelCase__			       =     np.linalg.svd(a__    )
								UpperCamelCase__			       =     svd_matrix[:, 0:dimensions]
								UpperCamelCase__			       =     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       _UpperCamelCase       ():






				"""simple docstring"""





				UpperCamelCase__			       =     np.array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7]]    )
				UpperCamelCase__			       =     np.array([0, 0, 0, 1, 1]    )
				UpperCamelCase__			       =     2
				UpperCamelCase__			       =     2

				# Assert that the function raises an AssertionError if dimensions > classes
				with pytest.raises(a__    ) as error_info:
								UpperCamelCase__			       =     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       _UpperCamelCase       ():






				"""simple docstring"""





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

				with pytest.raises(a__    ) as error_info:
								UpperCamelCase__			       =     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()











def       _UpperCamelCase       (a__				:dict    ):






							"""simple docstring"""





							UpperCamelCase__			       =     set()
							# To detect a back edge, keep track of vertices currently in the recursion stack
							UpperCamelCase__			       =     set()
							return any(
							    node not in visited and depth_first_search(a__				,     a__				,     a__				,     a__    )
							    for node in graph    )





def       _UpperCamelCase       (a__				:dict				,     a__				:int				,     a__				:set				,     a__				:set    ):






							"""simple docstring"""





							visited.add(a__    )
							rec_stk.add(a__    )

							for node in graph[vertex]:
														if node not in visited:
																					if depth_first_search(a__				,     a__				,     a__				,     a__    ):
																												return True
														elif node in rec_stk:
																					return True

    # The node needs to be removed from recursion stack before function ends
							rec_stk.remove(a__    )
							return False


if __name__ == "__main__":
					from doctest import testmod

					testmod()




