
"""simple docstring"""




class 			snake_case  :

							def __init__(self							,							SCREAMING_SNAKE_CASE_     ):

									"""simple docstring"""







									SCREAMING_SNAKE_CASE_    			=			set_counts
									SCREAMING_SNAKE_CASE_    			=			max(SCREAMING_SNAKE_CASE_     )
									SCREAMING_SNAKE_CASE_    			=			len(SCREAMING_SNAKE_CASE_     )
									SCREAMING_SNAKE_CASE_    			=			[1] * num_sets
									SCREAMING_SNAKE_CASE_    			=			list(range(SCREAMING_SNAKE_CASE_     )     )

							def _lowercase       (self							,							SCREAMING_SNAKE_CASE_							,							SCREAMING_SNAKE_CASE_     ):

									"""simple docstring"""







									SCREAMING_SNAKE_CASE_    			=			self.get_parent(SCREAMING_SNAKE_CASE_     )
									SCREAMING_SNAKE_CASE_    			=			self.get_parent(SCREAMING_SNAKE_CASE_     )

									if src_parent == dst_parent:
											return False

									if self.ranks[dst_parent] >= self.ranks[src_parent]:
											self.set_counts[dst_parent] += self.set_counts[src_parent]
											SCREAMING_SNAKE_CASE_    			=			0
											SCREAMING_SNAKE_CASE_    			=			dst_parent
											if self.ranks[dst_parent] == self.ranks[src_parent]:
													self.ranks[dst_parent] += 1
											SCREAMING_SNAKE_CASE_    			=			self.set_counts[dst_parent]
									else:
											self.set_counts[src_parent] += self.set_counts[dst_parent]
											SCREAMING_SNAKE_CASE_    			=			0
											SCREAMING_SNAKE_CASE_    			=			src_parent
											SCREAMING_SNAKE_CASE_    			=			self.set_counts[src_parent]

									SCREAMING_SNAKE_CASE_    			=			max(self.max_set							,							SCREAMING_SNAKE_CASE_     )
									return True







							def _lowercase       (self							,							SCREAMING_SNAKE_CASE_     ):

									"""simple docstring"""







									if self.parents[disj_set] == disj_set:
											return disj_set
									SCREAMING_SNAKE_CASE_    			=			self.get_parent(self.parents[disj_set]     )
									return self.parents[disj_set]

"""simple docstring"""




import logging

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

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



def 							_lowerCamelCase			(			__a     ):
		return input_array.reshape((input_array.size, 1)     )



def 							_lowerCamelCase			(			__a,				__a,				__a     ):
		SCREAMING_SNAKE_CASE_    			=			np.nan
		for i in range(__a     ):
				SCREAMING_SNAKE_CASE_    			=			features[:, labels == i]
				SCREAMING_SNAKE_CASE_    			=			data.mean(1     )
				# Centralize the data of class i
				SCREAMING_SNAKE_CASE_    			=			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)
						SCREAMING_SNAKE_CASE_    			=			np.dot(__a,				centered_data.T     )

		return covariance_sum / features.shape[1]



def 							_lowerCamelCase			(			__a,				__a,				__a     ):
		SCREAMING_SNAKE_CASE_    			=			features.mean(1     )
		SCREAMING_SNAKE_CASE_    			=			np.nan
		for i in range(__a     ):
				SCREAMING_SNAKE_CASE_    			=			features[:, labels == i]
				SCREAMING_SNAKE_CASE_    			=			data.shape[1]
				SCREAMING_SNAKE_CASE_    			=			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)
						SCREAMING_SNAKE_CASE_    			=			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,				__a     ):

		# Check if the features have been loaded
		if features.any():
				SCREAMING_SNAKE_CASE_    			=			features.mean(1     )
				# Center the dataset
				SCREAMING_SNAKE_CASE_    			=			features - np.reshape(__a,				(data_mean.size, 1)     )
				SCREAMING_SNAKE_CASE_    			=			np.dot(__a,				centered_data.T     ) / features.shape[1]
				SCREAMING_SNAKE_CASE_			,SCREAMING_SNAKE_CASE_    			=			np.linalg.eigh(__a     )
				# Take all the columns in the reverse order (-1), and then takes only the first
				SCREAMING_SNAKE_CASE_    			=			eigenvectors[:, ::-1][:, 0:dimensions]
				# Project the database on the new space
				SCREAMING_SNAKE_CASE_    			=			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,				__a,				__a,				__a     ):
		assert classes > dimensions

		# Check if features have been already loaded
		if features.any:
				SCREAMING_SNAKE_CASE_			,SCREAMING_SNAKE_CASE_    			=			eigh(
				    covariance_between_classes(__a,				__a,				__a     ),				covariance_within_classes(__a,				__a,				__a     ),				)
				SCREAMING_SNAKE_CASE_    			=			eigenvectors[:, ::-1][:, :dimensions]
				SCREAMING_SNAKE_CASE_			,SCREAMING_SNAKE_CASE_			,SCREAMING_SNAKE_CASE_    			=			np.linalg.svd(__a     )
				SCREAMING_SNAKE_CASE_    			=			svd_matrix[:, 0:dimensions]
				SCREAMING_SNAKE_CASE_    			=			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			(			):
		# Create dummy dataset with 2 classes and 3 features
		SCREAMING_SNAKE_CASE_    			=			np.array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7]]     )
		SCREAMING_SNAKE_CASE_    			=			np.array([0, 0, 0, 1, 1]     )
		SCREAMING_SNAKE_CASE_    			=			2
		SCREAMING_SNAKE_CASE_    			=			2

		# Assert that the function raises an AssertionError if dimensions > classes
		with pytest.raises(__a     ) as error_info:
				SCREAMING_SNAKE_CASE_    			=			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			(			):
		SCREAMING_SNAKE_CASE_    			=			np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]     )
		SCREAMING_SNAKE_CASE_    			=			2
		SCREAMING_SNAKE_CASE_    			=			np.array([[6.9_2_8_2_0_3_2_3, 8.6_6_0_2_5_4_0_4, 1_0.3_9_2_3_0_4_8_5], [3.0, 3.0, 3.0]]     )

		with pytest.raises(__a     ) as error_info:
				SCREAMING_SNAKE_CASE_    			=			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()